论文标题
验证Prandtl边界层Ansatz，用于稳定的电力，并具有移动的物理边界
Verification of Prandtl boundary layer ansatz for the steady electrically conducting fluids with a moving physical boundary
论文作者
论文摘要
在本文中，我们关注的是prandtl边界层扩展的有效性，该解决方案在域$ \ {（x，y）\ in [0，l] \ times \ times \ ntime \ mathb {r} y = y = y = y = y = y = y = y = n y = y = y = y = n y = y = y = y = y = y = y = y = y = n y y = n y y = y = n y y = y = n y = n y y = y = n y y = n y = 0. As a direct consequence, even though there exist strong boundary layers, the inviscid type limit is still established for the solutions of 2D steady viscous incompressible MHD equations in Sobolev spaces provided that the following three assumptions hold: the hydrodynamics and magnetic Reynolds numbers take the same order in term of the reciprocal of a small parameter $ε$, the tangential component of the magnetic field does not degenerate near the boundary and the ratio磁场切向分量的强度和速度的切向成分很小。并且错误项以$ l^\ infty $ sense估算。
In this paper, we are concerned with the validity of Prandtl boundary layer expansion for the solutions to two dimensional (2D) steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0, L]\times\mathbb{R}_+\}$ with a moving flat boundary $\{Y=0\}$. As a direct consequence, even though there exist strong boundary layers, the inviscid type limit is still established for the solutions of 2D steady viscous incompressible MHD equations in Sobolev spaces provided that the following three assumptions hold: the hydrodynamics and magnetic Reynolds numbers take the same order in term of the reciprocal of a small parameter $ε$, the tangential component of the magnetic field does not degenerate near the boundary and the ratio of the strength of tangential component of magnetic field and tangential component of velocity is suitably small. And the error terms are estimated in $L^\infty$ sense.
