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

Xiaolei Dong; Xiaolei Dong

doi:10.3934/era.2026068

Electronic Research Archive

2026, Volume 34, Issue 3: 1506-1523. doi: 10.3934/era.2026068

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Research article

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

Xiaolei Dong ^,

School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China

Received: 03 December 2025 Revised: 27 January 2026 Accepted: 04 February 2026 Published: 13 February 2026

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 $\phi(z)$ 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.
- MHD boundary layer equations,
- local well-posedness,
- analytic space
Citation: Xiaolei Dong. Well-posedness of the 3D MHD boundary layer equations in an analytic space[J]. Electronic Research Archive, 2026, 34(3): 1506-1523. doi: 10.3934/era.2026068

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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 $\phi(z)$ 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.

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