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

Yonghui Zou; Xin Xu; An Gao; Yonghui Zou; Xin Xu; An Gao

doi:10.3934/math.2023503

AIMS Mathematics

2023, Volume 8, Issue 4: 9933-9964. doi: 10.3934/math.2023503

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Research article

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

Yonghui Zou ¹,
Xin Xu ¹,
An Gao ^{2
,
,}

1.
School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
2.
Linyi Senior School of Finance and Economics, Linyi 276000, China

Received: 17 October 2022 Revised: 04 January 2023 Accepted: 18 January 2023 Published: 23 February 2023
MSC : 35Q30, 35Q35, 76D10

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.
- thermal boundary layer equations,
- Oleinik's monotonicity condition,
- local well-posedness
Citation: Yonghui Zou, Xin Xu, An Gao. Local well-posedness to the thermal boundary layer equations in Sobolev space[J]. AIMS Mathematics, 2023, 8(4): 9933-9964. doi: 10.3934/math.2023503

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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.

References

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