论文标题
等离子体 - vacuum界面上的弱非线性表面波
Weakly nonlinear surface waves on the plasma-vacuum interface
论文作者
论文摘要
我们考虑了理想不可压缩的磁性流动力学中的等离子体 - vacuum界面的自由边界问题。与经典的陈述不同，真空磁场遵守前马克斯韦尔动力学的Div-Curl系统，我们不忽略真空区域中的位移电流，而是考虑电气和磁场的麦克斯韦方程。我们的目的是在该等离子体界面问题的弱非线性状态下构建高度振荡的表面波解。 在分段恒定背景状态的必要且充分的稳定性条件下，当初始不连续性显示高频振荡时，我们以任何任意大的准确性构建近似解决方案，以在三个空间维度中以三个空间维度的自由边界问题构建近似解决方案。此外，这种近似表面波具有非平凡的残留非振荡成分。
We consider the free boundary problem for a plasma--vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement, where the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric and magnetic fields. Our aim is to construct highly oscillating surface wave solutions in weakly nonlinear regime to this plasma--vacuum interface problem. Under a necessary and sufficient stability condition for a piecewise constant background state, we construct approximate solutions at any arbitrarily large order of accuracy to the free boundary problem in three space dimensions when the initial discontinuity displays high frequency oscillations. Moreover, such approximate surface waves have nontrivial residual non-oscillatory components.
