Well-posedness of the 3D MHD boundary layer equations in an analytic space

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Abstract

The objective of this paper is to investigate the local well-posedness of analytic solutions to the three-dimensional (3D) magnetohydrodynamic (MHD) boundary layer equations without structural assumptions. Specifically, the general initial data are required to be real-analytic in the tangential variables (x,y) and satisfy Sobolev regularity in the normal variable z. We first adopt a variable transformation involving ϕ(z) to homogenize the boundary conditions and eliminate resulting high- order terms. Additionally, we employ delicate energy estimates combined with Gauss weight functions to control linearly growth terms.

Keywords

MHD boundary layer equations / local well-posedness / analytic space

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