论文标题
磁效应对2D MHD边界层方程的溶解度，在Sobolev空间中没有电阻率
Magnetic effects on the solvability of 2D MHD boundary layer equations without resistivity in Sobolev spaces
论文作者
论文摘要
在本文中，我们关注的是对2D不可压缩的MHD系统的边界层方程的溶解性的磁效应，而无需电阻率。 MHD边界层由源自不可压缩的粘性MHD系统得出的PrandTL类型方程描述，而在速度的无滑动边界条件下没有电阻率。假设最初的切向磁场不会退化，则证明了Sobolev空间中的局部时间良好，在速度场上没有单调性条件。此外，我们表明，如果切向磁场剪切层在一个点上退化，则在Sobolev设置中，剪切层周围的线性MHD边界层系统在同一点的初始速度剪切流中是非分基的，但要在Sobolev设置中进行了不当。
In this paper, we are concerned with the magnetic effect on the Sobolev solvability of boundary layer equations for the 2D incompressible MHD system without resistivity. The MHD boundary layer is described by the Prandtl type equations derived from the incompressible viscous MHD system without resistivity under the no-slip boundary condition on the velocity. Assuming that the initial tangential magnetic field does not degenerate, a local-in-time well-posedness in Sobolev spaces is proved without the monotonicity condition on the velocity field. Moreover, we show that if the tangential magnetic field shear layer is degenerate at one point, then the linearized MHD boundary layer system around the shear layer profile is ill-posed in the Sobolev settings provided that the initial velocity shear flow is non-degenerately critical at the same point.
