Communications in Mathematical Sciences

Volume 22 (2024)

Number 5

Global regularity criteria of the 3D MHD-Boussinesq equations without thermal diffusion

Pages: 1347 – 1360

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n5.a7

Authors

Zhengguang Guo (School of Mathematics and Statistics, Huaiyin Normal University, Huaian, Jiangsu, China)

Zunzun Zhang (Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang, China)

Caidi Zhao (Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang,China)

Abstract

We study the global regularity for the three dimensional incompressible magnetohydrodynamic-Boussinesq (MHD-Boussinesq) equations. By establishing some sufficient regularity conditions in terms of partial components of velocity and magnetic fields, we prove that solutions to the MHD-Boussinesq equations without thermal diffusivity will not blow-up in any finite time.

Keywords

MHD-Boussinesq equations, regularity criteria, partial components

2010 Mathematics Subject Classification

35B65, 35Q35, 76D05

Full Text (PDF format)

This work was partially supported by Natural Science Foundation of Jiangsu Province (BK20201478), by the Qing Lan Project of Jiangsu Universities, by the National Natural Science Foundation of China (11971356, 12371245), and by the Key project of Zhejiang Province’s Natural Science Foundation with No. LZ24A010005.

Received 5 June 2022

Received revised 1 August 2023

Accepted 22 November 2023

Published 15 July 2024