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This special issue is dedicated to Professor Hideo Kozono, Waseda University, on the occasion of his 60th birthday.
Hideo Kozono was born in Yokohama, Japan on November 29, 1958. In 1987, he earned his doctorate degree from Hokkaido University under the supervision of Shozo Koshi. At that time, he was also visiting Tokyo Institute of Technology and studying under Atsushi Inoue. In that same year, he was appointed to an assistant professorship at Nagoya University. In 1991, he was promoted to an associate professor at Kyushu University. In 1993, he returned to Nagoya University and remained there until 1999. In 1999, he was promoted to a full professor at Tohoku University, where he then spent the next 13 years. In 2012, he moved to Waseda University, where he is currently a professor. He has also held a professorship at Tohoku Univerisity since 2018.
From September 1988 to July 1990 and from March 1996 to July 1996, he received a grant from the Alexander von Humboldt Foundation and carried out research visits to University of Paderborn. Since those visits, he has maintained close friendships and research collaborations with many German researchers, especially with Reinhard Farwig and Hermann Sohr.
He published more than 140 research papers and made numerous and important contributions to the functional analytic research on equations in fluid mechanics and to harmonic analysis. He started his research with the analysis of 2D incompressible Euler equations in a time dependent domain [1] and the MHD equations for an incompressible fluid [2, 3]. Then, he studied the asymptotic behavior of the solutions to the incompressible Navier–Stokes equations in bounded or unbounded domains [4,5,6,7,8,9,10,11,12] jointly with Tohru Ozawa, Takayoshi Ogawa, and Hermann Sohr. The Navier–Stokes system has been one of his main subjects up to the present. Jointly with Hermann Sohr and Masao Yamazaki, he found the relation between the net force exerted on the obstacle and the \(L^3\) integrability of stationary solutions to the 3D Navier–Stokes equations and Stokes equations in exterior domains [13, 14]. Later, he also found the relation between the net force and asymptotic decay rate with respect to the time variable of non-stationary solutions to the 3D Navier–Stokes equations in exterior domains [15, 16]. These results showed that the weak \(L^3\) space is more important than the \(L^3\) space for the research of solutions to the 3D Navier–Stokes equations in exterior domains.
In the mid-1990s, Kozono succeeded in proving the uniqueness of the Leray–Hopf weak solutions in the endpoint space of Serrin’s class \(L^{\infty }(0,T;L^n)\) jointly with Hermann Sohr [17]. Also, with Sohr, he proved the regularity of the Leray–Hopf weak solutions in \(L^{\infty }(0,T;L^n)\) under some additional conditions [18].
Jointly with Mitsuhiro Nakao, in [19], he introduced a new approach for the study of time-periodic solutions to the Navier–Stokes equations in unbounded domains by the use of an integral equation defined on an infinite half-line. Their approach enables time-periodic solutions to be investigated by modern functional analytic methods and operator theory.
At the same time, Kozono started to apply harmonic analysis techniques to the study of nonlinear partial differential equations, mainly for the Navier–Stokes equations and obtained many important results. Jointly with Masao Yamazaki, in [20, 21], he introduced new function spaces of Besov-Morrey type and proved the well-posedness of the Navier–Stokes equations in those spaces, which we now call Kozono-Yamazaki spaces. In the mid-1990s, the Kozono-Yamazaki space \(N^{n/p-1}_{p,q,\infty }\) was the largest class for the global well-posedness of the Navier–Stokes equations. Also with Yamazaki, he established the \(L^p_w\) (weak \(L^p\)) theory for the exterior Navier–Stokes problem, and obtained its well-posedness, as well as stability results [22,23,24,25,26,27].
He also established new bilinear estimates and critical Sobolev inequalities in BMO, Besov, and Triebel-Lizorkin spaces [28,29,30,31] jointly with Takayoshi Ogawa, Yasushi Taniuchi, and Yukihiro Shimada. As applications, he obtained new regularity and extension criteria for the Navier–Stokes and Euler equations.
From 2005, Kozono published an outstanding series of joint works with Reinhard Farwig and Hermann Sohr [32,33,34,35,36,37]. In those papers, he established the so-called \(\tilde{L}^q\) theory on the Navier–Stokes equations in very general unbounded domains that may have unbounded boundaries. Among these papers, he showed the existence of weak solutions which satisfy several regularity properties. This result was published in Acta Mathematica, and now regarded as one of the fundamental theories on the Navier–Stokes equations.
From 2008, jointly with Yoshie Sugiyama, Kozono also obtained important results on the Keller–Segel system in the \(L^p\) setting [38,39,40,41,42,43]. Together with Masanori Miura, they also showed the wel-posedness of the Keller–Segel system coupled with Navier–Stokes fluids [44, 45].
From 2009, jointly with Taku Yanagisawa, he has been working on the structure of vector fields in multi-connected domains. They generalized the div-curl lemma and identified a relation between the solvability of the stationary Navier–Stokes equations and the topological structure of the domains [46,47,48,49,50,51]. They went on to generalize these results to exterior domains with Anton Seyfert, Matthias Hieber and Senjo Shimizu [52,53,54,55].
Recently, jointly with Yutaka Terasawa and Yuta Wakasugi, he proved Liouville-type theorems for the stationary Navier–Stokes equations [56, 57]. It is notable that their Liouville-type theorems are applicable to some 2D unbounded domains including exterior domains, while many known Liouville-type theorems for 2D Navier–Stokes equations were proven only for the whole plane \(\mathbb R^2\).
Jointly with Senjo Shimizu, he also proved the well-posedness of non-stationary Navier–Stokes equations with external forces in Lorentz spaces or Besov spaces with scaling invariant norms by establishing the maximal Lorentz regularity (in the time variable ) on the Stokes equations in Besov spaces [58,59,60,61,62]. Their existence theorem enables us to handle such singular data as the Dirac measure and the single layer potential supported on the sphere.
Very recently, jointly with Reinhard Farwig and David Wegmann, he started to investigate the incompressible Navier–Stokes equations in domains with moving boundaries [63]. He also proved the maximal regularity on the Stokes equations with a moving boundary. Together with Kazuyuki Tsuda, they succeeded in constructing time-periodic solutions in \(L^q\) spaces to the Navier–Stokes equations in a bounded domain with a moving boundary [64]. As for other important papers of Kozono, we refer the readers to [66,67,68,69,70,71,72,73,74,75].
Kozono has received several prizes for his remarkable achievements in mathematics. In 2002, he received the Siebold prize from the Federal Republic of Germany. In 2014, he was awarded the Autumn Prize of the Mathematical Society of Japan for his contributions on “Harmonic analytic research on stationary and nonstationary problems for the incompressible Navier–Stokes equations”. In 2016, he also received the “Commendation for Science and Technology" from the Japanese Minister of Education, Culture, Sports, Science and Technology.
Kozono has also contributed to the mathematical community and been a member of several committees. Most significantly, he was the president of the Mathematical Society of Japan from May 2017 to May 2019. From April 2017, he has been one of coordinators of the JSPS Japanese-German Graduate Externship “Mathematical Fluid Dynamics”, jointly operated by Waseda University, The University of Tokyo, and TU Darmstadt, which is founded by JSPS and DFG. Since 2021, he is the chairman of Japan’s National Committee for the International Mathematical Union. He is now recognized as one of the leading mathematicians in the field of partial differential equations.
This volume is inspired by the international conference “Mathematical Fluid Mechanics and Related Topics,” held on September 5–7, 2018 at Tokyo Institute of Technology, on the occasion of Professor Kozono’s 60th birthday, which was organized by Hideyuki Miura, Takahiro Okabe, Tomoyuki Suzuki, Ryo Takada, Yasushi Taniuchi, Erika Ushikoshi, and Hidemitsu Wadade, all his former doctoral students. We express our gratitude to the organizers and participants of that conference and especially to all the authors who contributed to this volume during this difficult time of the COVID-19 pandemic.
To end this preface, we would like to thank the referees for their critical reviews and useful comments on the original papers. We would especially like to thank Professor Hideo Kozono for an everlasting friendship and important mathematics.
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Guest editors:
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Kazuhiro Ishige
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Tohru Ozawa
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Senjo Shimizu
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Yasushi Taniuchi
Japanese “Kagami-Biraki” ceremony at the banquet of Conference dedicated to Professor Kozono’s 60th birthday (2018). From left to right, Reinhard Farwig, Takaaki Nishida, Hideo Kozono, Shigetoshi Kuroda, Yukio Kaneda, and Hisashi Okamoto.
References
Kozono, K.: On existence and uniqueness of a global classical solution of the two-dimensional Euler equation in a time-dependent domain. J. Differ. Equ. 57, 275–302 (1985)
Kozono, H.: On the energy decay of a weak solution of the MHD equations in a three-dimensional exterior domain. Hokkaido Math. J. 16(2), 151–166 (1987)
Kozono, H.: Weak and classical solutions of the two-dimensional magnetohydrodynamic equations. Tohoku Math. J. 41(3), 471–488 (1989)
Kozono, K.: Strong Solution for the Navier–Stokes Flow in the Half-space, The Navier–Stokes equations (Oberwolfach, 1988), 84–86, Lecture Notes in Math., vol. 1431. Springer, Berlin (1990)
Kozono, K., Ozawa, T.: Stability in \(L^r\) for the Navier–Stokes flow in an n-dimensional bounded domain. J. Math. Anal. Appl. 152(1), 35–45 (1990)
Kozono, H., Sohr, H.: New a priori estimates for the Stokes equations in exterior domains. Indiana Univ. Math. J. 40(1), 1–27 (1991)
Kozono, H., Ogawa, T., Sohr, H.: Asymptotic behaviour in \(L^r\) for weak solutions of the Navier–Stokes equations in exterior domains. Manuscr. Math. 74(3), 253–275 (1992)
Kozono, H., Ogawa, T.: Some \(L^p\) estimate for the exterior Stokes flow and an application to the nonstationary Navier–Stokes equations. Indiana Univ. Math. J. 41(3), 789–808 (1992)
Kozono, H., Ogawa, T.: Decay properties of strong solutions for the Navier–Stokes equations in two-dimensional unbounded domains. Arch. Ration. Mech. Anal. 122(1), 1–17 (1993)
Kozono, H., Ogawa, T.: Two-dimensional Navier–Stokes flow in unbounded domains. Math. Ann. 297(1), 1–31 (1993)
Kozono, H., Ogawa, T.: Global strong solution and its decay properties for the Navier–Stokes equations in three-dimensional domains with noncompact boundaries. Math. Z. 216(1), 1–30 (1994)
Kozono, H., Ogawa, T.: On stability of Navier–Stokes flows in exterior domains. Arch. Ration. Mech. Anal. 128(1), 1–31 (1994)
Kozono, H., Sohr, H.: On stationary Navier–Stokes equations in unbounded domains. Ricerche Mat. 42(1), 69–86 (1993)
Kozono, H., Sohr, H., Yamazaki, M.: Representation formula, net force and energy relation to the stationary Navier–Stokes equations in 3-dimensional exterior domains. Kyushu J. Math. 51(1), 239–260 (1997)
Kozono, H.: \(L^1\) -solutions of the Navier–Stokes equations in exterior domains. Math. Ann. 312(2), 319–340 (1998)
Kozono, H.: Rapid time-decay and net force to the obstacles by the Stokes flow in exterior domains. Math. Ann. 320(4), 709–730 (2001)
Kozono, H., Sohr, H.: Remark on uniqueness of weak solutions to the Navier–Stokes equations. Analysis 16(3), 255–271 (1996)
Kozono, H., Sohr, H.: Regularity criterion of weak solutions to the Navier–Stokes equations. Adv. Differ. Equ. 2(4), 535–554 (1997)
Kozono, H., Nakao, M.: Periodic solutions of the Navier–Stokes equations in unbounded domains. Tohoku Math. J. 48, 33–50 (1996)
Kozono, H., Yamazaki, M.: Semilinear heat equations and the Navier–Stokes equation with distributions in new function spaces as initial data. Commun. Partial Differ. Equ. 19, 959–1014 (1994)
Kozono, H., Yamazaki, M.: The stability of small stationary solutions in Morrey spaces of the Navier–Stokes equation. Indiana Univ. Math. J. 44(4), 1307–1336 (1995)
Kozono, H., Yamazaki, M.: The Navier–Stokes Exterior Problem with Cauchy Data in the Space \(L^{n,\infty }\), Advances in Geometric Analysis and Continuum Mechanics (Stanford, CA, 1993), pp. 160–174. Int. Press, Cambridge (1995)
Kozono, H., Yamazaki, M.: Local and global unique solvability of the Navier–Stokes exterior problem with Cauchy data in the space \(L^{n,\infty }\). Houston J. Math. 21(4), 755–799 (1995)
Kozono, H., Yamazaki, M.: Exterior problem for the stationary Navier–Stokes equations in the Lorentz space. Math. Ann. 310(2), 279–305 (1998)
Kozono H., Yamazaki, M.: Exterior Problem for the Navier–Stokes Equations, Existence, Uniqueness and Stability of Stationary Solutions, Theory of the Navier–Stokes Equations, 86–98, Ser. Adv. Math. Appl. Sci., vol. 47. World Sci. Publ., River Edge (1998)
Kozono, H., Yamazaki, M.: On a larger class of stable solutions to the Navier–Stokes equations in exterior domains. Math. Z. 228(4), 751–785 (1998)
Kozono, H., Yamazaki, M.: Uniqueness criterion of weak solutions to the stationary Navier–Stokes equations in exterior domains. Nonlinear Anal. Ser. Theory Methods 38(8), 959–970 (1999)
Kozono, H., Taniuchi, Y.: Bilinear estimates in BMO and the Navier–Stokes equations. Math. Z. 235(1), 173–194 (2000)
Kozono, H., Taniuchi, Y.: Limiting case of the Sobolev inequality in BMO, with application to the Euler equations. Commun. Math. Phys. 214(1), 191–200 (2000)
Kozono, H., Ogawa, T., Taniuchi, Y.: The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations. Math. Z. 242(2), 251–278 (2002)
Kozono, H.: Shimada, Y, Bilinear estimates in homogeneous Triebel–Lizorkin spaces and the Navier–Stokes equations. Math. Nachr. 276, 63–74 (2004)
Farwig, R., Kozono, H., Sohr, H.: An \(L^q\)-approach to Stokes and Navier–Stokes equations in general domains. Acta Math. 195, 21–53 (2005)
Farwig, R., Kozono, H., Sohr, H.: On the Helmholtz decomposition in general unbounded domains. Arch. Math. 88(3), 239–248 (2007)
Farwig, R., Kozono, H., Sohr, H.: The Stokes Resolvent Problem in General Unbounded Domains, Kyoto Conference on the Navier–Stokes Equations and their Applications, 79–91, RIMS Kokyuroku Bessatsu, B1, Res. Inst. Math. Sci. (RIMS ), Kyoto (2007)
Farwig, R., Kozono, H., Sohr, H.: Maximal Regularity of the Stokes Operator in General Unbounded Domains of \(\mathbb{R}^n\), Functional Analysis and Evolution Equations, pp. 257–272. Birkhauser, Basel (2008)
Farwig, R., Kozono, H., Sohr, H.: On the Stokes operator in general unbounded domains. Hokkaido Math. J. 38(1), 111–136 (2009)
Farwig, R., Kozono, H., Sohr, H.: Stokes Semigroups, Strong, Weak, and Very Weak Solutions for General Domains, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, pp. 419–459. Springer, Cham (2018)
Kozono, H., Sugiyama, Y.: Local existence and finite time blow-up of solutions in the 2-D Keller–Segel system. J. Evol. Equ. 8(2), 353–378 (2008)
Kozono, H., Sugiyama, Y.: The Keller–Segel system of parabolic-parabolic type with initial data in weak \(L^{n/2}(\mathbb{R}^n)\) and its application to self-similar solutions. Indiana Univ. Math. J. 57(4), 1467–1500 (2008)
Kozono, H., Sugiyama, Y.: Global strong solution to the semi-linear Keller–Segel system of parabolic- parabolic type with small data in scale invariant spaces. J. Differ. Equ. 247(1), 1–32 (2009)
Kozono, H., Sugiyama, Y.: Strong solutions to the Keller–Segel system with the weak \(L^2\) initial data and its application to the blow-up rate. Math. Nachr. 283(5), 732–751 (2010)
Kozono, H., Sugiyama, Y., Wachi, T.: Existence and uniqueness theorem on mild solutions to the Keller–Segel system in the scaling invariant space. J. Differ. Equ. 252(2), 1213–1228 (2012)
Kozono, H., Sugiyama, Y., Yahagi, Y.: Existence and uniqueness theorem on weak solutions to the parabolic-elliptic Keller–Segel system. J. Differ. Equ. 253(7), 2295–2313 (2012)
Kozono, H., Miura, M., Sugiyama, Y.: Existence and uniqueness theorem on mild solutions to the Keller–Segel system coupled with the Navier–Stokes fluid. J. Funct. Anal. 270(5), 1663–1683 (2016)
Kozono, H., Miura, M., Sugiyama, Y.: Time global existence and finite time blow-up criterion for solutions to the Keller–Segel system coupled with the Navier–Stokes fluid. J. Differ. Equ. 267(9), 5410–5492 (2019)
Kozono, H., Yanagisawa, T.: Leray’s problem on the stationary Navier–Stokes equations with inhomogeneous boundary data. Math. Z. 262(1), 27–39 (2009)
Kozono, H., Yanagisawa, T.: Global Div-Curl lemma on bounded domains in \(\mathbb{R}^3\). J. Funct. Anal. 256(11), 3847–3859 (2009)
Kozono, H., Yanagisawa, T.: \(L^r\)-variational inequality for vector fields and the Helmholtz–Weyl decomposition in bounded domains. Indiana Univ. Math. J. 58(4), 1853–1920 (2009)
Kozono, H., Yanagisawa, T.: Nonhomogeneous boundary value problems for stationary Navier–Stokes equations in a multiply connected bounded domain. Pac. J. Math. 243(1), 127–150 (2009)
Kozono, H., Yanagisawa, T.: Global compensated compactness theorem for general differential operators of first order. Arch. Ration. Mech. Anal. 207(3), 879–905 (2013)
Kozono, H., Yanagisawa, T.: \(L^r\)-Helmholtz decomposition and its application to the Navier–Stokes equations, Lectures on the analysis of nonlinear partial differential equations. Part 3, Morningside Lect. Math., 3, pp. 237–290. Int. Press, Somerville (2013)
Hieber, M., Kozono, H., Seyfert, A., Shimizu, S., Yanagisawa, T.: A characterization of harmonic \(L^r\)-vector fields in two-dimensional exterior domains. J. Geom. Anal. 30(4), 3742–3759 (2020)
Hieber, M., Kozono, H., Seyfert, A., Shimizu, S., Yanagisawa, T.: The Helmholtz-Weyl decomposition of \(L^r\) vector fields for two dimensional exterior domains. J. Geom. Anal. 31(5), 5146–5165 (2021)
Hieber, M., Kozono, H., Seyfert, A., Shimizu, S., Yanagisawa, T.: \(L^r\)-Helmholtz–Weyl decomposition for three dimensional exterior domains. J. Funct. Anal. 281(8), 109144 (2021)
Hieber, M., Kozono, H., Seyfert, A., Shimizu, S., Yanagisawa, T.: A characterization of harmonic \(L^r\)-vector fields in three dimensional exterior domains. J. Geom. Anal. 32(7), 206 (2022)
Kozono, H., Terasawa, Y., Wakasugi, Y.: A remark on Liouville-type theorems for the stationary Navier–Stokes equations in three space dimensions. J. Funct. Anal. 272(2), 804–818 (2017)
Kozono, H., Terasawa, Y., Wakasugi, Y.: Finite energy of generalized suitable weak solutions to the Navier–Stokes equations and Liouville-type theorems in two dimensional domains. J. Differ. Equ. 265(4), 1227–1247 (2018)
Kozono, H., Shimizu, S.: Navier–Stokes equations with external forces in Lorentz spaces and its application to the self-similar solutions. J. Math. Anal. Appl. 458(2), 1693–1708 (2018)
Kozono, H., Shimizu, S.: Strong Solutions of the Navier–Stokes Equations with Singular Data, Mathematical Analysis in Fluid Mechanics-Selected Recent Results, Contemp. Math., vol. 710, pp. 163–173. American Mathematical Society (2018)
Kozono, H., Shimizu, S.: Navier–Stokes equations with external forces in time-weighted Besov spaces. Math. Nachr. 291(11–12), 1781–1800 (2018)
Kozono, H., Shimizu, S.: Strong solutions of the Navier–Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces. J. Funct. Anal. 276(3), 896–931 (2019)
Kaneko, K., Kozono, H., Shimizu, S.: Stationary solution to the Navier–Stokes equations in the scaling invariant Besov space and its regularity. Indiana Univ. Math. J. 68(3), 857–880 (2019)
Farwig, R., Kozono, H., Wegmann, D.: Maximal regularity of the Stokes operator in an exterior domain with moving boundary and application to the Navier–Stokes equations. Math. Ann. 375(3–4), 949–972 (2019)
Farwig, R., Kozono, H., Tsuda, K., Wegmann, D.: The time periodic problem of the Navier–Stokes equations in a bounded domain with moving boundary. Nonlinear Anal. Real World Appl. 61 (2021)
Kozono, H.: On a decay property of weak solution for semilinear evolution equation of parabolic type and its applications. Math. Z. 196(1), 21–38 (1987)
Kozono, H.: Global \(L^n\)-solution and its decay property for the Navier–Stokes equations in half-space \(R^n_+\). J. Differ. Equ. 79(1), 79–88 (1989)
Kozono, H.: Uniqueness and Regularity of Weak Solutions to the Navier–Stokes Equations, Recent Topics on Mathematical Theory of Viscous Incompressible fluid (Tsukuba, 1996), Lecture Notes Numer. Appl. Anal., vol. 16, pp. 161–208. Kinokuniya, Tokyo (1998)
Kozono, H.: Removable singularities of weak solutions to the Navier–Stokes equations. Commun. Partial Differ. Equ. 23(5–6), 949–966 (1998)
Kim, H., Kozono, H.: A removable isolated singularity theorem for the stationary Navier–Stokes equations. J. Differ. Equ. 220(1), 68–84 (2006)
Heck, H., Kim, H., Kozono, H.: On the stationary Navier–Stokes flows around a rotating body. Manuscr. Math. 138(3–4), 315–345 (2012)
Kim, H., Kozono, H.: On the stationary Navier–Stokes equations in exterior domains. J. Math. Anal. Appl. 395(2), 486–495 (2012)
Farwig, R., Kozono, H., Yanagisawa, T.: Leray’s inequality in general multi-connected domains in \(\mathbb{R}^n\). Math. Ann. 354(1), 137–145 (2012)
Kozono, H., Ushikoshi, E.: Hadamard variational formula for the Green’s function of the boundary value problem on the Stokes equations. Arch. Ration. Mech. Anal. 208(3), 1005–1055 (2013)
Heck, H., Kim, H., Kozono, H.: Weak solutions of the stationary Navier–Stokes equations for a viscous incompressible fluid past an obstacle. Math. Ann. 356(2), 653–681 (2013)
Kozono, H., Yanagisawa, T.: Generalized Lax–Milgram theorem in Banach spaces and its application to the elliptic system of boundary value problems. Manuscr. Math. 141(3–4), 637–662 (2013)
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Appendices
Mathematical Fluid Mechanics and Related Topics
In honor of Professor Hideo Kozono’s sixtieth birthday—Sept 5–7, 2018
Lecture Theatre, West Lecture Bldg. 1, Tokyo Insitute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, JAPAN
–Program–
\(\underline{\mathbf{September 5\ (Wed.)}}\)
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09:50\(\sim \)10:00 Opening
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10:00\(\sim \)10:40 Reinhard Farwig (Technische Universität Darmstadt)
Global attractors for non-autonomous quasi-geostrophic equations in \(R^2\)
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10:50\(\sim \)11:30 Taku Yanagisawa (Nara Woman’s University)
A geometric characterization of the spaces of harmonic \(L^r\)-vector fields
over exterior domains
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11:50\(\sim \)12:30 Tai-Peng Tsai (University of British Columbia)
Global Navier–Stokes flows for non-decaying initial data with slowly
decaying oscillation
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12:30\(\sim \)14:00 Lunch Time
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14:00\(\sim \)14:40 Senjo Shimizu (Kyoto University)
Necessary and sufficient condition on initial data for solutions in the Serrin
class of the Navier–Stokes equations
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14:50\(\sim \)15:30 Lorenzo Brandolese (Université Lyon 1)
Characterization of solutions to Navier–Stokes with sharp algebraic decay
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16:00\(\sim \)16:40 Toshiaki Hishida (Nagoya University)
\(L^q\)-\(L^r\) estimate of the evolution operator arising from fluid motion past
a rotating obstacle, with applications to the Navier–
Stokes initial value problem
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16:50\(\sim \)17:30 Takayuki Kobayashi (Osaka University)
Stability problem for a constant equilibrium to the compressible Navier–
Stokes–Korteweg system
\(\underline{\mathbf{September 6\ (Thur.)}}\)
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10:00\(\sim \)10:40 Hi Jun Choe (Yonsei University)
Blow up criteria of compressible Navier–Stokes flow
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10:50\(\sim \)11:30 Michael Růžička (Albert-Ludwigs-Universität Freiburg)
On the regularity of the steady p-Stokes problem
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11:50\(\sim \)12:30 Horst Heck (Bern University of Applied Sciences)
Stability for Calderon-type inverse problems
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12:30\(\sim \)14:00 Lunch Time
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14:00\(\sim \)14:40 Takayoshi Ogawa (Tohoku University)
Well-posedness of the initial value problem for incompressible Navier–
Stokes equations under the Lagrangian coordinate
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14:50\(\sim \)15:30 Dongho Chae (Chung-Ang University)
On the Type I blow-up for the incompressible Euler equations
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16:00\(\sim \)16:40 Tohru Ozawa (Waseda University)
Improved Hardy inequalities
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19:00\(\sim \) Banquet
\(\underline{\mathbf{September 7 \ (Fri.)}}\)
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10:00\(\sim \)10:40 Paolo Maremonti (Università degli Studi della Campania Luigi
Vanvitelli)
Global existence of solutions with non-decaying initial data 2D(3D)-
Navier–Stokes IBVP in half-plane(space)
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10:50\(\sim \)11:30 Matthias Hieber (Technische Universität Darmstadt)
A Journey Through the World of Periodic Solutions: From the Keller–
Segel Model to Geophysical Flows
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11:50\(\sim \)12:30 Yoshiyuki Kagei (Kyushu University)
Large time behavior of solutions to the compressible Navier–Stokes
equations in a cylinder under the slip boundary condition
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12:30\(\sim \)14:00 Lunch Time
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14:00\(\sim \)14:40 Helmut Abels (Universität Regensburg)
Well-posedness of a Navier–Stokes/mean curvature flow system
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14:50\(\sim \)15:30 Hyunseok Kim (Sogang University)
Existence and uniqueness results for weak solutions of elliptic equations
with singular drifts in weak Lebesgue spaces
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15:30\(\sim \) closing
Organizing Committee
Hideyuki Miura (Tokyo Institute of Technology) Takahiro Okabe (Osaka University) Tomoyuki Suzuki (Kanagawa University) Ryo Takada (Kyushu University) Yasushi Taniuchi (Shinshu University) Erika Ushikoshi (Yokohama National University) Hidemitsu Wadade (Kanazawa University)
This conference is supported by
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JSPS Grant-in-Aid for Scientific Research (S) JP16H06339 (Hideo Kozono)
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JSPS Grant-in-Aid for Scientific Research (S) JP25220702 (Takayoshi Ogawa)
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JSPS Grant-in-Aid for Scientific Research (A) JP15H02058 (Kazuhiro Ishige)
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JSPS Grant-in-Aid for Scientific Research (C) JP16K05228 (Yasushi Taniuchi)
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JSPS Grant-in-Aid for Scientific Research (C) JP17K05312 (Hideyuki Miura)
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JSPS Grant-in-Aid for Young Scientists (A) JP15H05436 (Ryo Takada)
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JSPS Grant-in-Aid for Young Scientists (B) JP16K21056 (Hidemitsu Wadade)
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JSPS Grant-in-Aid for Young Scientists (B) JP17K14215 (Takahiro Okabe)
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JSPS Grant-in-Aid for Early-Career Scientists No.18K13439 (Erika Ushikoshi)
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Ishige, K., Ozawa, T., Shimizu, S. et al. Preface. Partial Differ. Equ. Appl. 3, 53 (2022). https://doi.org/10.1007/s42985-022-00184-1
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DOI: https://doi.org/10.1007/s42985-022-00184-1