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Research Article | Open Access

A priori estimates for the free boundary problem of incompressible inviscid Boussinesq and MHD-Boussinesq equations without heat diffusion

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
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Abstract

For all physical spatial dimensions n = 2 and 3, we establish a priori estimates of Sobolev norms for free boundary problem of inviscid Boussinesq and MHD-Boussinesq equations without heat diffusion under the Taylor-type sign condition on the initial free boundary. It is different from MHD equations because the energy of the system is not conserved.

Keywords

free boundary problemBoussinesqMHD-Boussinesqincompressible flowsa priori estimates
CLC number: 35K59, 76W05

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 6074-6094
DOI: 10.3934/math.2023307

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Zhang W. A priori estimates for the free boundary problem of incompressible inviscid Boussinesq and MHD-Boussinesq equations without heat diffusion. AIMS Mathematics, 2023, 8(3): 6074-6094. https://doi.org/10.3934/math.2023307

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Received: 09 September 2022
Revised: 13 December 2022
Accepted: 21 December 2022
Published: 15 March 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)