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• W2726565577 abstract "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." @default.
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• W2726565577 date "2018-07-17" @default.
• W2726565577 modified "2023-10-12" @default.
• W2726565577 title "MHD Boundary Layers Theory in Sobolev Spaces Without Monotonicity I: Well-Posedness Theory" @default.
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• W2726565577 doi "https://doi.org/10.1002/cpa.21763" @default.
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