GLOBAL STABILITY OF LARGE SOLUTIONS TO THE 3D MAGNETIC BÉNARD PROBLEM

doi:10.1007/s10473-022-0212-y

Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (2): 588-610.doi: 10.1007/s10473-022-0212-y

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GLOBAL STABILITY OF LARGE SOLUTIONS TO THE 3D MAGNETIC BÉNARD PROBLEM

Xulong QIN¹, Hua QIU², Zheng-an YAO³

1. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
2. Department of Mathematics, South China Agricultural University, Guangzhou 510642, China;
3. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Received:2020-07-21 Revised:2021-05-22 Online:2022-04-25 Published:2022-04-22
Supported by:
Qin is supported partially by NSFC (11571380, 11971497, 11871230) and Natural Science Foundation of GuangDong Province (2019B151502041); Qiu is supported partially by NSFC (11126266), Natural Science Foundation of GuangDong Province (2016A030313390) and SCAU Fund for High-level University Building; Yao was supported partially by NSFC (11971496).

Abstract

CLC Number:

35B65

Xulong QIN, Hua QIU, Zheng-an YAO. GLOBAL STABILITY OF LARGE SOLUTIONS TO THE 3D MAGNETIC BÉNARD PROBLEM[J].Acta mathematica scientia,Series B, 2022, 42(2): 588-610.

Trendmd

[1] Cheng J, Du L. On two-dimensional magnetic Bénard problem with mixed partial viscosity. J Math Fluid Mech, 2015, 17:769-797
[2] Galdi G P, Padula M A. A new approach to energy theory in the stability of fluid motion. Arch Ration Mech Anal, 1990, 110:187-286
[3] Kato T. Strong L^p-solutions of the Navier-Stokes equation in R^m with applications to weak solutions. Math Z, 1984, 187:471-480
[4] Koch H, Tataru D. Well-posedness for the Navier-Stokes equations. Adv Math, 2001, 157:22-35
[5] Li X, Jiu Q. Global L² stability of large solutions to the 3D Boussinesq equations. Acta Math Sin (Chin Series), 2010, 53:171-186
[6] Ma L. Global regularity results for the 2(1/2) magnetic Bénard system with mixed partial viscosity. Appl Anal, 2019, 98:1143-1164
[7] Manna U, Panda A A. Local existence and blow-up criterion for the two and three dimensional ideal magnetic Bénard problem. Electron J Differential Equations, 2020, 91:26 pp
[8] Mulone G. Rionero S. Necessary and sufficient conditions for nonlinear stability in the magnetic Bénard problem. Arch Ration Mech Anal, 2003, 166:197-218
[9] Nakamura M A. On the magnetic Bénard problem. J Fac Sci Univ Tokyo Sect IA Math, 1991, 38:359-393
[10] Ponce G, Racke R, Sideris T C, Titi E S. Global stability of large solutions to the 3D Navier-Stokes equations. Commun Math Phys, 1994, 159:329-341
[11] Schonbek M, Schonbek T P, Suli E. The long time behavior of solutions to MHD equations. Math Ann, 1996, 304:717-756
[12] Seregin G A. On the local regularity of suitable weak solutions of the Navier-Stokes equations (in Russian). Uspekhi Mat Nauk, 2007, 62:149-168
[13] Stein E M. Singular Integrals and Differentiability Properties of Functions. Princeton NJ:Princeton University Press, 1970
[14] Ye Z. Global regularity of the 2D magnetic Bénard system with partial dissipation. Adv Differential Equations, 2018, 23:193-238
[15] Zhang Z, Tang T. Global regularity for a special family of axisymmetric solutions to the three-dimensional magnetic Bénard problem. Appl Anal, 2018, 97:2533-2543
[16] Zhao C, Li K. Global L² stability of large solutions to the 3D MHD equations. Acta Math Sin (Chin Series), 2001, 44:961-976
[17] Zhou Y, Fan J, Nakamura G. Global Cauchy problem for a 2D magnetic Bénard problem with zero thermal conducivity. Appl Math Lett, 2013, 26:627-630

GLOBAL STABILITY OF LARGE SOLUTIONS TO THE 3D MAGNETIC BÉNARD PROBLEM

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