Abstract
This paper concerns improving Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system, in the sense of multiplying certain negative powers of scaling invariant norms.
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References
H. Beirão da Veiga: A new regularity class for the Navier-Stokes equations in ℝn. Chin. Ann. Math., Ser. B 16 (1995), 407–412.
P. Constantin, C. Fefferman: Direction of vorticity and the problem of global regularity for the Navier-Stokes equations. Indiana Univ. Math. J. 42 (1993), 775–789.
L. Escauriaza, G.A. Serëgin, V. Shverak: L 3,∞-solutions of Navier-Stokes equations and backward uniqueness. Russ. Math. Surv. 58 (2003), 211–250; translation from Usp. Mat. Nauk 58 (2003), 3–44.
H. Fujita, T. Kato: On the Navier-Stokes initial value problem. I. Arch. Ration. Mech. Anal. 16 (1964), 269–315.
E. Hopf: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4 (1951), 213–321. (In German.)
T. Kato: Strong L p-solutions of the Navier-Stokes equation in ℝm, with applications to weak solutions. Math. Z. 187 (1984), 471–480.
J. Leray: Sur le mouvement d’un liquide visqueux emplissant l’espace. Acta Math. 63 (1934), 193–248. (In French.)
G. Prodi: Un teorema di unicità per le equazioni di Navier-Stokes. Ann. Mat. Pura Appl., IV. Ser. 48 (1959), 173–182. (In Italian.)
J. C. Robinson, J. L. Rodrigo, W. Sadowski: The Three-Dimensional Navier-Stokes Equations. Classical Theory. Cambridge Studies in Advanced Mathematics 157, Cambridge University Press, Cambridge, 2016.
R. Schoen, S.-T. Yau: Lectures on Differential Geometry. Conference Proceedings and Lecture Notes in Geometry and Topology 1, International Press, Cambridge, 1994.
J. Serrin: On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Ration. Mech. Anal. 9 (1962), 187–195.
H. Sohr, W. von Wahl: On the singular set and the uniqueness of weak solutions of the Navier-Stokes equations. Manuscr. Math. 49 (1984), 27–59.
C. V. Tran, X. Yu: Depletion of nonlinearity in the pressure force driving Navier-Stokes flows. Nonlinearity 28 (2015), 1295–1306.
C. V. Tran, X. Yu: Pressure moderation and effective pressure in Navier-Stokes flows. Nonlinearity 29 (2016), 2290–3005.
C. V. Tran, X. Yu: Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations. J. Math. Phys. 58 (2017), 011501, 10 pages.
A. Vasseur: Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity. Appl. Math., Praha 54 (2009), 47–52.
Z. Zhang, X. Yang: Navier-Stokes equations with vorticity in Besov spaces of negative regular indices. J. Math. Anal. Appl. 440 (2016), 415–419.
Z. Zhang, Y. Zhou: On regularity criteria for the 3D Navier-Stokes equations involving the ratio of the vorticity and the velocity. Comput. Math. Appl. 72 (2016), 2311–2314.
Y. Zhou: Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain. Math. Ann. 328 (2004), 173–192.
Y. Zhou: A new regularity criterion for the Navier-Stokes equations in terms of the direction of vorticity. Monatsh. Math. 144 (2005), 251–257.
Y. Zhou: Direction of vorticity and a new regularity criterion for the Navier-Stokes equations. ANZIAM J. 46 (2005), 309–316.
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Zujin Zhang is partially supported by the National Natural Science Foundation of China (grant nos. 11761009, 11501125) and the Natural Science Foundation of Jiangxi (grant no. 20171BAB201004).
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Zhang, Z., Wu, C. & Zhou, Y. On Ratio Improvement of Prodi-Serrin-Ladyzhenskaya Type Regularity Criteria for the Navier-Stokes System. Czech Math J 69, 1165–1175 (2019). https://doi.org/10.21136/CMJ.2019.0128-18
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DOI: https://doi.org/10.21136/CMJ.2019.0128-18