Yudovich type solution for the two dimensional Euler-Boussinesq system with critical dissipation and general source term

Oussama Melkemi; Mohammed S. Abdo; Wafa Shammakh; Hadeel Z. Alzumi; Oussama Melkemi; Mohammed S. Abdo; Wafa Shammakh; Hadeel Z. Alzumi

doi:10.3934/math.2023944

AIMS Mathematics

2023, Volume 8, Issue 8: 18566-18580. doi: 10.3934/math.2023944

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Research article

Yudovich type solution for the two dimensional Euler-Boussinesq system with critical dissipation and general source term

1.
Laboratory of partial differential equations and applications, the University of Batna 2, Batna 05000, Algeria
2.
Department of Mathematics, Hodeidah University, P.O. Box 3114, Al Hudaydah, Yemen
3.
Department of Mathematics, University of Jeddah, Faculty of Science, Jeddah, Saudi Arabia

Received: 19 March 2023 Revised: 14 May 2023 Accepted: 19 May 2023 Published: 01 June 2023
MSC : 35Q35, 35B65, 76D03

The present article investigates the two-dimensional Euler-Boussinesq system with critical fractional dissipation and general source term. First, we show that this system admits a global solution of Yudovich type, and as a consequence, we treat the regular vortex patch issue.
- Boussinesq system,
- weak solutions,
- Besov spaces,
- fractional dissipation,
- regular vortex patch
Citation: Oussama Melkemi, Mohammed S. Abdo, Wafa Shammakh, Hadeel Z. Alzumi. Yudovich type solution for the two dimensional Euler-Boussinesq system with critical dissipation and general source term[J]. AIMS Mathematics, 2023, 8(8): 18566-18580. doi: 10.3934/math.2023944

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Abstract

The present article investigates the two-dimensional Euler-Boussinesq system with critical fractional dissipation and general source term. First, we show that this system admits a global solution of Yudovich type, and as a consequence, we treat the regular vortex patch issue.

References

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