论文标题
适合在理想可压缩MHD中移动表面张力的移动界面的适合性
Well-posedness for Moving Interfaces with Surface Tension in Ideal Compressible MHD
论文作者
论文摘要
我们研究了与表面张力的界面的局部良好性，该界面将完美传导的无粘性流体与真空分开。流体流程受三维理想可压缩磁性流动力学（MHD）的方程式，而真空磁场和电场应该满足前马克斯韦尔方程。流体和真空磁场与界面相切。这使得与特征自由边界的非线性双曲线耦合问题。我们引入了一些合适的正则化，以建立线性化问题的可解决性和驯服估计。将线性良好的结果与修改后的NASH-序列迭代方案相结合，我们证明了非线性问题解决方案的局部存在和唯一性。 Secchi和Trakhinin所需的非共线性条件[非线性27（1）：105--169，2014]对于零表面张力的情况下，我们的结果是不必要的，这验证了表面张力对理想可压缩MHD中移动真空接口的演化的稳定作用。
We study the local well-posedness for an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equations of three-dimensional ideal compressible magnetohydrodynamics (MHD), while the vacuum magnetic and electric fields are supposed to satisfy the pre-Maxwell equations. The fluid and vacuum magnetic fields are tangential to the interface. This renders a nonlinear hyperbolic-elliptic coupled problem with a characteristic free boundary. We introduce some suitable regularization to establish the solvability and tame estimates for the linearized problem. Combining the linear well-posedness result with a modified Nash--Moser iteration scheme, we prove the local existence and uniqueness of solutions of the nonlinear problem. The non-collinearity condition required by Secchi and Trakhinin [Nonlinearity 27(1): 105--169, 2014] for the case of zero surface tension becomes unnecessary in our result, which verifies the stabilizing effect of surface tension on the evolution of moving vacuum interfaces in ideal compressible MHD.
