Yudovich type solution for the two dimensional Euler-Boussinesq system with critical dissipation and general source term-Reference-Cited by-同舟云学术

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

Published:2023 Issue:8 Volume:8 Page:18566-18580
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Melkemi Oussama¹,Abdo Mohammed S.²,Shammakh Wafa³,Alzumi Hadeel Z.³

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference32 articles.

1. H. Abidi, T. Hmidi, S. Keraani, On the global well-posedness for the axisymmetric Euler equations, Math. Ann., 347 (2010), 15–41. https://doi.org/10.1007/s00208-009-0425-6

2. S. Alinhac, P. Gérard, Opérateurs pseudo-différentiels et théorème de Nash-Moser, InterEditions, Paris, 1991. https://doi.org/10.1051/978-2-7598-0282-1

3. H. Bahouri, J. Y. Chemin, R. Danchin, Fourier analysis and nonlinear partial differential equations, Springer Berlin, Heidelberg, 2011. https://doi.org/10.1007/978-3-642-16830-7

4. A. L. Bertozzi, P. Constantin, Global regularity for vortex patches, Commun. Math. Phys., 152 (1993), 19–28. https://doi.org/10.1007/BF02097055

5. Y. Brenier, Optimal transport, convection, magnetic relaxation and generalized Boussinesq equations, J. Nonlinear Sci., 19 (2009), 547–570. https://doi.org/10.1007/s00332-009-9044-3

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