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

Wei Zhang; Wei Zhang

doi:10.3934/math.2023307

AIMS Mathematics

2023, Volume 8, Issue 3: 6074-6094. doi: 10.3934/math.2023307

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

Wei Zhang ^,

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

Received: 09 September 2022 Revised: 13 December 2022 Accepted: 21 December 2022 Published: 29 December 2022
MSC : 35K59, 76W05

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.
- free boundary problem,
- Boussinesq,
- MHD-Boussinesq,
- incompressible flows,
- a priori estimates
Citation: Wei Zhang. A priori estimates for the free boundary problem of incompressible inviscid Boussinesq and MHD-Boussinesq equations without heat diffusion[J]. AIMS Mathematics, 2023, 8(3): 6074-6094. doi: 10.3934/math.2023307

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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.

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