GLOBAL WELL-POSEDNESS FOR 3D-AXISYMMETRIC ANISOTROPIC BOUSSINESQ SYSTEM WITH STRATIFICATION EFFECTS.

Oussama Melkemi

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GLOBAL WELL-POSEDNESS FOR 3D-AXISYMMETRIC ANISOTROPIC BOUSSINESQ SYSTEM WITH STRATIFICATION EFFECTS.

Oussama Melkemi

¹ Department of Mathematics, University of Batna 2

Academic Editor: Manuel De Leon

Published: 28 April 2023 by MDPI in The 1st International Online Conference on Mathematics and Applications session Mathematical Physics

https://doi.org/10.3390/IOCMA2023-14379 (registering DOI)

Abstract:

In this work, we study the Cauchy problem of the 3d-Anisotropic Boussinesq system with Horizontal dissipation and stratification effect for axisymmetric data. This system couples the Navier-stokes equation with a non-homogenous transport-diffusion equation. More precisely, we prove that this kind of system admits a unique global solution belongs to the Anisotropic Sobolev spaces.

Keywords: Global well-posedness, Anisotropic Sobolev spaces, Global regularity

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Oussama Melkemi