论文标题
不可压缩的不可压力电阻MHD的全球自由接口问题的适应性
Global Well-posedness of Free Interface Problems for the incompressible Inviscid Resistive MHD
论文作者
论文摘要
我们考虑了均匀的非休闲磁场印象深刻的水平周期性平板中的等离子体 - vacuum界面问题。下等离子体区域受不可压缩的无粘性和电阻性MHD的约束，上真空区域受到前马克斯韦方程的控制，并且在自由界面上考虑了表面张力的效果。该问题的全局良好性，补充了物理边界条件，在平衡周围建立，并且该溶液几乎呈指数呈指数衰减。我们的结果揭示了磁场的强大稳定作用，因为自由体外不可压缩的欧拉方程的全局良好性，而没有无关假设，在平衡周围是未知的。这里的主要观察结果之一是由于电阻率和横向磁场而导致流体涡度的诱导阻尼结构。获得了类似的血浆血浆界面问题的全局良好性，在那里真空被另一个等离子体代替。
We consider the plasma-vacuum interface problem in a horizontally periodic slab impressed by a uniform non-horizontal magnetic field. The lower plasma region is governed by the incompressible inviscid and resistive MHD, the upper vacuum region is governed by the pre-Maxwell equations, and the effect of surface tension is taken into account on the free interface. The global well-posedness of the problem, supplemented with physical boundary conditions, around the equilibrium is established, and the solution is shown to decay to the equilibrium almost exponentially. Our results reveal the strong stabilizing effect of the magnetic field as the global well-posedness of the free-boundary incompressible Euler equations, without the irrotational assumption, around the equilibrium is unknown. One of the key observations here is an induced damping structure for the fluid vorticity due to the resistivity and transversal magnetic field. A similar global well-posedness for the plasma-plasma interface problem is obtained, where the vacuum is replaced by another plasma.
