Well-posedness for the Linearized Free Boundary Problem of Incompressible Ideal Magnetohydrodynamics Equations.
Well-posedness for the Linearized Free Boundary Problem of Incompressible Ideal Magnetohydrodynamics Equations.
复制标题
DOI：
10.1016/j.jde.2021.07.030
复制
发表时间：
2019-11
期刊：
影响因子：
--
通讯作者：
Chengchun Hao;T. Luo
中科院分区：
文献类型：
--
作者：
Chengchun Hao;T. Luo
研究了有界区域内不可压缩理想磁流体力学方程线性化自由边界问题的适定性理论。我们用拉格朗日坐标系下的速度场和变形张量来表示磁场，并将其代入动量方程，得到一个初始磁场仅作为参数的速度方程。然后，将速度方程与时间导数为速度的位置向量场线性化。在这个公式中，一个关键的思想是利用磁场的李氏导数，利用磁场与自由边界的切向和无散度的优势。本文为研究不受图约束的一般自由边界的泰勒符号型条件下理想磁流体动力学方程自由边界问题的适定性的几何方法的发展计划作出了贡献。
The well-posedness theory is studied for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors in Lagrangian coordinates, and substitute it into the momentum equation to get an equation of the velocity in which the initial magnetic field serves only as a parameter. Then, the velocity equation is linearized with respect to the position vector field whose time derivative is the velocity. In this formulation, a key idea is to use the Lie derivative of the magnetic field taking the advantage that the magnetic field is tangential to the free boundary and divergence free. This paper contributes to the program of developing geometric approaches to study the well-posedness of free boundary problems of ideal magnetohydrodynamics equations under the condition of Taylor sign type for general free boundaries not restricted to graphs.