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Research Article | Open Access

Local existence of solutions to the 2D MHD boundary layer equations without monotonicity in Sobolev space

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

In this work, we investigated the local existence of the solutions to the 2D magnetohy-drodynamic (MHD) boundary layer equations on the half plane by energy methods in weighted Sobolev space. Compared to the existence of solutions to the classical Prandtl equations where the monotonicity condition of the tangential velocity plays an important role, we used the initial tangential magnetic field with a lower bound δ > 0 instead of the monotonicity condition of the tangential velocity.

Keywords

MHD boundary layer equationsthe existence of solutionsthe energy methodthe weighted sobolev space
CLC number: 35M33, 35Q35, 76D03, 76D10, 76W05

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AIMS Mathematics
Volume 9 Issue 3,
March 2024
Pages 5294-5329
DOI: 10.3934/math.2024256

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Cite this article:
Dong X. Local existence of solutions to the 2D MHD boundary layer equations without monotonicity in Sobolev space. AIMS Mathematics, 2024, 9(3): 5294-5329. https://doi.org/10.3934/math.2024256

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Received: 15 November 2023
Revised: 19 January 2024
Accepted: 19 January 2024
Published: 15 March 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)