Skip to main content
SpringerLink
Log in

Two-dimensional Navier-Stokes flow in unbounded domains

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Adams, R.A.: Sobolev spaces. New York: Academic Press 1975

    Google Scholar 

  2. Borchers, W., Miyakawa, T.:L 2 decay for the Navier-Stokes flow in half spaces. Math. Ann.282, 139–155 (1988)

    Google Scholar 

  3. Borchers, W., Miyakawa, T.: AlgebraicL 2 decay for Navier-Stokes flows in exterior domains. Acta Math.165, 189–227 (1990)

    Google Scholar 

  4. Borchers, W., Miyakawa, T.:L 2 decay for the Navier-Stokes flows in unbounded domains with application to exterior stationary flows. Arch. Ration. Mech. Anal.118, 273–295 (1992)

    Google Scholar 

  5. Borchers, W., Sohr, H.: On the semigroup of the Stokes operator for exterior domains inL q-spaces. Math. Z.196, 415–425 (1987)

    Google Scholar 

  6. Borchers, W., Varnhorn, W.: On the boundedness of the Stokes semigroup in two-dimensional exterior domains. (Preprint)

  7. Finn, R.: Stationary solutions of the Navier-Stokes equations. Proc. Symp. Appl. Math.19 (1965)

  8. Finn, R.: On exterior stationary problem for the Navier-Stokes equations and associated perturbation problems. Arch. Ration. Mech. Anal.19, 363–406 (1965)

    Google Scholar 

  9. Fujita, H., Kato, T.: On the Navier-Stokes initial value problem 1. Arch. Ration. Mech. Anal.46, 269–315 (1964)

    Google Scholar 

  10. Fujita, H., Morimoto, H.: On fractional powers of the Stokes operator. Proc. Japan Acad.46, 1141–1143 (1970)

    Google Scholar 

  11. Giga, Y.: Domains of fractional powers of the Stokes operator inL r spaces. Arch. Ration. Mech. Anal.89, 251–265 (1985)

    Google Scholar 

  12. Giga, Y., Miyakawa, T.: Solution inL r of the Navier-Stokes initial value problem. Arch. Ration. Mech. Anal.89, 267–281 (1985)

    Google Scholar 

  13. Giga, Y., Sohr, H.: On the Stokes operator in exterior domains. J. Fac. Sci., Univ. Tokyo, Sect. IA Math.36, 103–130 (1989)

    Google Scholar 

  14. Heywood, J.G.: The Navier-Stokes equations: On the existence, regularity and decay of solutions. Indiana Univ. Math. J.29, 639–681 (1980)

    Google Scholar 

  15. Itô, S.: Fundamental solutions of parabolic differential equations and boundary value problems. Jap. J. Math.27, 55–102 (1957)

    Google Scholar 

  16. Iwashita, H.:L q-Lr estimates for solutions of nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problem inL q spaces. Math. Ann.285, 265–288 (1989)

    Google Scholar 

  17. Kajikiya, R., Miyakawa, T.: OnL 2 decay of weak solutions of the Navier-Stokes equations in ℝn. Math. Z.192, 135–148 (1986)

    Google Scholar 

  18. Kato, T., Fujita, H.: On the nonstationary Navier-Stokes system. Rend. Semin. Mat. Univ. Padova32, 243–260 (1962)

    Google Scholar 

  19. Kato, T.: StrongL p-solutions of the Navier-Stokes equation ℝm, with applications to weak solutions. Math. Z.187, 471–480 (1984)

    Google Scholar 

  20. Kozono, H.: GrobalL n-solution and its decay property for the Navier-Stokes equations in half-space ℝ n+ . J. Differ. Equations79, 79–88 (1989)

    Google Scholar 

  21. Kozono, H., Ogawa, T., Sohr, H.: Asymptotic behavior inL r for turbulent solutions of the Navier-Stokes equations in exterior domains. Manuscr. Math.74, 253–275 (1992)

    Google Scholar 

  22. Kuroda, S.T.: Spectral theory 2 (Iwanami Kôza Kiso Sûgaku) (in Japanese). Tokyo: Iwanami 1979

    Google Scholar 

  23. Ladyzhenskaya, O.A.: The mathematical theory of viscous incompressible flow. New York: Gordon and Breach 1969

    Google Scholar 

  24. Leray, J.: Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math.63, 193–248 (1934)

    Google Scholar 

  25. Masuda, K.: On the stability of incompressible viscous fluid motions past object. J. Math. Soc. Japan27, 294–327 (1975)

    Google Scholar 

  26. Masuda, K.: Weak solutions of the Navier-Stokes equations. Tôhoku Math. J.36, 623–646 (1984)

    Google Scholar 

  27. Miyakawa, T.: On nonstationary solutions of the Navier-Stokes equations in an exterior domain. Hiroshima Math. J.12, 115–140 (1982)

    Google Scholar 

  28. Miyakawa, T., Sohr, H.: On energy inequality, smoothness and large time behavior inL 2 for weak solutions of the Navier-Stokes equations in exterior domains. Math. Z.199, 455–478 (1988)

    Google Scholar 

  29. Ogawa, T.: A proof of Trudinger's inequality and its application to nonlinear Schrödinger equations. Nonlinear Anal., Theory Methods Appl.14, 765–769 (1990)

    Google Scholar 

  30. Ogawa, T., Ozawa, T.: Trudinger type inequalities and uniqueness of weak solutions for the nonlinear Schrödinger mixed problem. J. Math. Anal. Appl.155, 531–540 (1991)

    Google Scholar 

  31. Prodi, G.: Un theorema di unicità per le equazioni di Navier-Stokes. Ann. Mat.48, 173–182 (1959)

    Google Scholar 

  32. Schonbek, M.E.:L 2 decay for weak solutions of the Navier-Stokes equations. Arch. Ration. Mech. Anal.88, 209–222 (1985)

    Google Scholar 

  33. Serrin, J.: The initial value problem for the Navier-Stokes equations. In: Longer, R. (ed.) Nonlinear problem, pp. 69–98. Madison: The University of Wisconsin Press 1960

    Google Scholar 

  34. Solonnikov, V.A.: General boundary value problems for systems which are elliptic in the sense of Douglis-Nirenberg 1. Am. Math. Soc. Transl.,56, 193–232 (1966)

    Google Scholar 

  35. Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton, NJ: Princeton University Press 1970

    Google Scholar 

  36. Tanabe, H.: Equations of evolution. London: Pitman 1979

    Google Scholar 

  37. Ukai, S.: A solution formula for the Stokes equations in ℝ n+ . Commun. Pure Appl. Math.40, 611–621 (1987)

    Google Scholar 

  38. von Wahl, W.: The equations of Navier-Stokes and abstract parabolic equations. Braunschweig Wiesbaden: Vieweg 1985

    Google Scholar 

  39. Wiegner, M.: Decay results for weak solutions of the Navier-Stokes equations in ℝn. J. Lond. Math. Soc.35, 303–313 (1987)

    Google Scholar 

  40. Wiegner, M.: Decay and stability inL p for strong solutions of the Cauchy problem for the Navier-Stokes equations. In: Heywood et al. (eds.) The Navier-Stokes equations, theory and numerical methods. (Lect. Notes Math., vol. 1431, pp. 95–99) Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  41. Yao Jing-Qi: Comportment à l'infini des solution d'une équation de Schrödinger nonlinéaires dans un domaine extérier. C. R. Acad. Sci., Paris15, 163–166 (1982)

    Google Scholar 

Download references

Author information

Author notes

  1. Hideo Kozono

    Present address: Department of Applied Physics, Nagoya University, Furô-chô, Chikusa-ku, 464-01, Nagoya, Japan

Authors and Affiliations

  1. Department of Mathematics, College of General Education, Kyushu University, Ropponmatsu, Chûô-ku, Fukuoka 810, Japan

    Hideo Kozono

  2. Department of Mathematics, Nagoya University, Furô-chô, Chikusa-ku, 464-01, Nagoya, Japan

    Takayoshi Ogawa

Authors
  1. Hideo Kozono
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Takayoshi Ogawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Professor Hiroki Tanabe on the occasion of his sixtieth birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kozono, H., Ogawa, T. Two-dimensional Navier-Stokes flow in unbounded domains. Math. Ann. 297, 1–31 (1993). https://doi.org/10.1007/BF01459486

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01459486

Mathematics Subject Classification (1991)

Search

Navigation