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Research Article | Open Access

Local well-posedness to the thermal boundary layer equations in Sobolev space

Yonghui Zou1, Xin Xu1, An Gao2( )
School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
Linyi Senior School of Finance and Economics, Linyi 276000, China
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Abstract

In this paper, we study the local well-posedness of the thermal boundary layer equations for the two-dimensional incompressible heat conducting flow with nonslip boundary condition for the velocity and Neumann boundary condition for the temperature. Under Oleinik's monotonicity assumption, we establish the local-in-time existence and uniqueness of solutions in Sobolev space for the boundary layer equations by a new weighted energy method developed by Masmoudi and Wong.

Keywords

thermal boundary layer equationsOleinik's monotonicity conditionlocal well-posedness
CLC number: 35Q30, 35Q35, 76D10

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AIMS Mathematics
Volume 8 Issue 4,
April 2023
Pages 9933-9964
DOI: 10.3934/math.2023503

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Cite this article:
Zou Y, Xu X, Gao A. Local well-posedness to the thermal boundary layer equations in Sobolev space. AIMS Mathematics, 2023, 8(4): 9933-9964. https://doi.org/10.3934/math.2023503

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Received: 17 October 2022
Revised: 04 January 2023
Accepted: 18 January 2023
Published: 15 April 2023
©2023 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)