|
正交曲线坐标系中三维不可压粘性MHD系统的大初值整体适定性
|
Abstract:
本文研究了正交曲线坐标系中三维不可压MHD系统在大光滑初值条件下的整体适定性。我们针对一类新的光滑大初值,建立了三维不可压粘性MHD系统Cauchy问题在正交曲线坐标系下的整体光滑解的存在性和唯一性。
This paper investigates the global well-posedness of the three-dimensional incompressible MHD system in orthogonal curvilinear coordinates with large smooth initial data. We establish the global existence and uniqueness of the smooth solutions to the Cauchy problem for the three-dimensional incompressible viscous MHD system in orthogonal curvilinear coordinates for a new class of the smooth large initial data.
[1] | Bachelor, G.K. (1967) An Introduction to Fluid Dynamics. Cambridge University Press. |
[2] | 谢树艺. 矢量分析与场论[M]. 北京: 高等教育出版社, 1978. |
[3] | Chae, D. and Kim, N. (1997) Axisymmetric Weak Solutions of the 3-D Euler Equations for Incompressible Fluid Flows. Nonlinear Analysis: Theory, Methods & Applications, 29, 1393-1404. https://doi.org/10.1016/s0362-546x(96)00186-1 |
[4] | He, C. and Xin, Z. (2005) On the Regularity of Weak Solutions to the Magnetohydrodynamic Equations. Journal of Differential Equations, 213, 235-254. https://doi.org/10.1016/j.jde.2004.07.002 |
[5] | Zhou, Y. (2005) Remarks on Regularities for the 3D MHD Equations. Discrete & Continuous Dynamical Systems, 12, 881-886. https://doi.org/10.3934/dcds.2005.12.881 |
[6] | 王术. Sobolev空间与偏微分方程引论[M]. 北京: 科学出版社, 2008. |
[7] | Sermange, M. and Temam, R. (1983) Some Mathematical Questions Related to the Mhd Equations. Communications on Pure and Applied Mathematics, 36, 635-664. https://doi.org/10.1002/cpa.3160360506 |
[8] | Nirenberg, L. (1959) On Elliptic Partial Differential Equations. The Annali della Scuola Normale Superiore di Pisa, 13, 115-162. |
[9] | Evans, L.C. (2010) Partial Differential Equations (Graduate Studies in Mathematics). 2nd Edition, American Mathematical Society. |
[10] | Duvaut, G. and Lions, J.L. (1972) Inéquations en thermoélasticité et magnétohydrodynamique. Archive for Rational Mechanics and Analysis, 46, 241-279. https://doi.org/10.1007/bf00250512 |
[11] | Lei, Z. (2015) Global Well-Posedness of Incompressible Magnetohydrodynamic Equations with Minimal Regularity. Communications on Pure and Applied Mathematics, 68, 1839-1891. |
[12] | Wang, Y. and Wang, M. (2019) Global Smooth Solutions to the 3D Incompressible Navier-Stokes Equations with Large Initial Data in Spherical Coordinates. Science China Mathematics, 62, 1743-1758. |
[13] | Deng, W. and Zhang, P. (2018) Large Time Behavior of Solutions to 3-D MHD System with Initial Data near Equilibrium. Archive for Rational Mechanics and Analysis, 230, 1017-1102. https://doi.org/10.1007/s00205-018-1265-x |
[14] | Ke, X., Yuan, B. and Xiao, Y. (2021) A Stability Problem for the 3D Magnetohydrodynamic Equations near Equilibrium. Acta Mathematica Scientia, 41, 1107-1118. https://doi.org/10.1007/s10473-021-0405-9 |