论文标题
可压缩电阻磁水动力学中自由边界问题的本地稳定性
Local Well-posedness of the Free-Boundary Problem in Compressible Resistive Magnetohydrodynamics
论文作者
论文摘要
我们证明了在雷利 - 泰勒物理标志条件下，在自由边缘问题的Sobolev空间中，在自由边缘问题的Sobolev空间中，可压缩电阻性等粒子MHD系统，该系统描述了具有磁性扩散的电磁场中自由体性可压缩等离子体的运动。我们使用Lagrangian坐标，并应用Coutand-Shkoller引入的切向平滑方法来构建近似解决方案。关键观察之一是Christodoulou-lindblad型椭圆估计与磁扩散不仅可以直接赋予磁场和流体压力的共同控制，而且还控制着洛伦兹力，这是能量功能中高阶期的洛伦兹力。
We prove the local well-posedness in Sobolev spaces of the free-boundary problem for compressible inviscid resistive isentropic MHD system under the Rayleigh-Taylor physical sign condition, which describes the motion of a free-boundary compressible plasma in an electro-magnetic field with magnetic diffusion. We use Lagrangian coordinates and apply the tangential smoothing method introduced by Coutand-Shkoller to construct the approximation solutions. One of the key observations is that the Christodoulou-Lindblad type elliptic estimate together with magnetic diffusion not only gives the common control of magnetic field and fluid pressure directly, but also controls the Lorentz force which is a higher order term in the energy functional.
