Na Wang
Beijing University of Technology, China
Title: The boundary layer problem on the incompressible MHD system with noncharacteristic Dirichlet boundary condition for velocity
Biography
Biography: Na Wang
Abstract
In this paper, we study the boundary layer and vanishing viscosity-diffusion limit problem for the incompressible magneto-hydrodynamic (MHD) system, which has the non-characteristic Dirichlet boundary condition for the velocity and the perfect conducting wall boundary condition for the magnetic field. Using the multiscale analysis and asymptotic expansion approach, we can obtain the inner function equations and boundary layer equations. By solving the boundary layer equations, we find that the velocity has the low order boundary layer, and the magnetic field has the high order boundary layer. Then we use the inner functions and the boundary layer functions to construct the approximate solutions. At last, utilizing the elaborate energy methods, we can strictly prove that the solutions of the viscous and diffuse MHD system can be approximated by the approximate solutions when the viscosity and diffusion coefficient tend to zero.
Recent Publications
1.Wang S, Wang B Y, Liu C D, Wang Na (2017) Boundary layer problem and zero viscosity-diffusion limit of the incompressible magnetohydrodynamic system with no-slip boundary conditions. Journal of Differential Equation doi: 10.1016/j.jde.2017.05.025.
2.Guo B L and Wang G W (2016) Vanishing viscosity limit for the 3D magnetohydrodynamic system with generalized Navier slip boundary conditions. Mathematical Methods in the Applied Sciences 39:4526-4534.
3.Wu Z L and Wang S (2015) Zero viscosity and diffusion vanishing limit of the incompressible magnetohydrodynamic system with perfectly conducting wall. Nonlinear Analysis: Real World Applications 24:50-60.
4.Xie X Q, Luo L and Li C M (2014) Boundary layer for MHD equations with the non-characteristic boundary conditions (in Chinese). Chinese Annals of Mathematics 35A(2):171-192.
5. Xiao Y L, Xin Z P and Wu J H (2009) Vanishing viscosity limit for the 3D magnetohydrodynamic system with a slip boundary condition. Journal of Functional Analysis 257:3375-3394.