GLOBAL-IN-TIME STABILITY OF 2D MHD BOUNDARY LAYER IN THE PRANDTL-HARTMANN REGIME

被引：25

作者：

Xie, Feng ^{[1
,2
]}

Yang, Tong ^{[1
,3
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, LSC MOE, Shanghai 200240, Peoples R China

[3] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 06期

关键词：

MHD boundary layer; Prandtl-Hartmann regime; global stability; analytic regularity; NAVIER-STOKES EQUATION; ZERO VISCOSITY LIMIT; WELL-POSEDNESS; ILL-POSEDNESS; ANALYTIC SOLUTIONS; MAGNETIC-FIELD; HALF-SPACE; EXISTENCE; SYSTEM; EULER;

D O I：

10.1137/18M1174969

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the global existence of solutions with analytic regularity to the 2D magnetohydrodynamic (MHD) boundary layer equations in the mixed Prandtl and Hartmann regime derived by formal multiscale expansion in [D. Gerard-Varet and M. Prestipino, Z. Angew. Math. Phys., 68 (2017), 76]. The analysis shows that the combined effect of the magnetic diffusivity and transverse magnetic field on the boundary leads to a linear damping on the tangential velocity field near the boundary. And this damping effect yields the global-in-time analytic norm estimate in the tangential space variable on the perturbation of the classical steady Hartmann profile.

引用

页码：5749 / 5760

页数：12

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