Uniform Estimate of Viscous Free-Boundary Magnetohydrodynamics with Zero Vacuum Magnetic Field
Uniform Estimate of Viscous Free-Boundary Magnetohydrodynamics with Zero Vacuum Magnetic Field
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DOI：
10.1137/16m1089794
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发表时间：
2014-09
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影响因子：
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通讯作者：
Donghyung Lee
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文献类型：
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作者：
Donghyung Lee
本文在$\mathbb{R}^3$中考虑真空条件下粘性自由边界磁流体力学，特别是当真空磁场为同零时。求解双曲型无粘方程组的消失极限是数学中的一个中心问题。但边界层行为发生在自由边界附近，因此存在时间$T^{\varepsilon} \rightarrow 0$为标准Sobolev空间中的运动粘度$\varepsilon\rightarrow 0$。灵感源自[N.]Masmoudi和F. Rousset, Arch。定量。械甲怪。分析的。， 223 (2017), pp. 301—417]，我们使用Sobolev正规空间来推导粘度的均匀规律性$\varepsilon$。最后，我们得到了自由边界上初始磁场为零和真空条件下无粘自由边界MHD的解。
We consider viscous free-boundary magnetohydrodynamics (MHD) under vacuum in $\mathbb{R}^3$, especially when the vacuum magnetic field is identically zero. It is a central problem in mathematics to perform the vanishing viscosity limit to get a solution of a hyperbolic inviscid system. However, boundary layer behavior happens near the free boundary, so the existence time $T^{\varepsilon} \rightarrow 0$ as the kinematic viscosity $\varepsilon\rightarrow 0$ in standard Sobolev space. Inspired by [N. Masmoudi and F. Rousset, Arch. Ration. Mech. Anal., 223 (2017), pp. 301--417], we use Sobolev conormal space to derive uniform regularity in viscosity $\varepsilon$. Finally, we get a solution of inviscid free-boundary MHD when the initial magnetic field is zero on the free boundary and in vacuum.