MHD Boundary Layers Theory in Sobolev Spaces Without Monotonicity I: Well‐Posedness Theory
MHD Boundary Layers Theory in Sobolev Spaces Without Monotonicity I: Well‐Posedness Theory
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DOI：
10.1002/cpa.21763
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发表时间：
2016-11
影响因子：
3
通讯作者：
Cheng-Jie Liu;Feng Xie;Tong Yang
中科院分区：
文献类型：
--
作者：
Cheng-Jie Liu;Feng Xie;Tong Yang
我们研究了MHD边界层的适定性理论。边界层方程由Prandtl型方程控制，该方程由不可压缩MHD系统导出，速度为无滑移边界条件，磁场为理想传导条件。在初始切向磁场不为零的假设下，我们建立了非线性MHD边界层方程局部时间解的存在唯一性。与经典普朗特方程的适定性理论相比，切向速度的单调性条件起着至关重要的作用，而MHD边界层不需要单调性条件。这从严格的数学上证明了磁场对磁流体边界层具有稳定作用的物理认识。© 2018 Wiley Periodicals，Inc.
We study the well‐posedness theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl‐type equations that are derived from the incompressible MHD system with non‐slip boundary condition on the velocity and perfectly conducting condition on the magnetic field. Under the assumption that the initial tangential magnetic field is not zero, we establish the local‐i‐time existence, uniqueness of solutions for the nonlinear MHD boundary layer equations. Compared with the well‐posedness theory of the classical Prandtl equations for which the monotonicity condition of the tangential velocity plays a crucial role, this monotonicity condition is not needed for the MHD boundary layer. This justifies the physical understanding that the magnetic field has a stabilizing effect on MHD boundary layer in rigorous mathematics. © 2018 Wiley Periodicals, Inc.