Volume 34, Issue 2
Conditional Regularity of Weak Solutions to the 3D Magnetic Bénard Fluid System

J. Part. Diff. Eq., 34 (2021), pp. 144-169.

Published online: 2021-05

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• Abstract

This paper concerns about the regularity conditions of weak solutions to the magnetic Bénard fluid system in $\mathbb{R}^3$. We show that a weak solution $(u,b,θ)(·,t)$ of the 3D magnetic Bénard fluid system defined in $[0,T),$ which satisfies some regularity requirement as $(u,b,θ),$ is regular in $\mathbb{R}^3×(0,T)$ and can be extended as a $C^∞$ solution beyond $T$.

• Keywords

Magnetic Bénard fluid system, regularity criteria, conditional regularity, Morrey-Campanato space, Besov space.

35B45, 35B65, 76D03, 35Q35, 76W05

mllpzh@126.com (Liangliang Ma)

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@Article{JPDE-34-144, author = {Liangliang and Ma and mllpzh@126.com and 16569 and Department of Applied Mathematics, Chengdu University of Technology, Chengdu 610059, China and Liangliang Ma}, title = {Conditional Regularity of Weak Solutions to the 3D Magnetic Bénard Fluid System}, journal = {Journal of Partial Differential Equations}, year = {2021}, volume = {34}, number = {2}, pages = {144--169}, abstract = {

This paper concerns about the regularity conditions of weak solutions to the magnetic Bénard fluid system in $\mathbb{R}^3$. We show that a weak solution $(u,b,θ)(·,t)$ of the 3D magnetic Bénard fluid system defined in $[0,T),$ which satisfies some regularity requirement as $(u,b,θ),$ is regular in $\mathbb{R}^3×(0,T)$ and can be extended as a $C^∞$ solution beyond $T$.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v34.n2.4}, url = {http://global-sci.org/intro/article_detail/jpde/19185.html} }
TY - JOUR T1 - Conditional Regularity of Weak Solutions to the 3D Magnetic Bénard Fluid System AU - Ma , Liangliang JO - Journal of Partial Differential Equations VL - 2 SP - 144 EP - 169 PY - 2021 DA - 2021/05 SN - 34 DO - http://doi.org/10.4208/jpde.v34.n2.4 UR - https://global-sci.org/intro/article_detail/jpde/19185.html KW - Magnetic Bénard fluid system, regularity criteria, conditional regularity, Morrey-Campanato space, Besov space. AB -

This paper concerns about the regularity conditions of weak solutions to the magnetic Bénard fluid system in $\mathbb{R}^3$. We show that a weak solution $(u,b,θ)(·,t)$ of the 3D magnetic Bénard fluid system defined in $[0,T),$ which satisfies some regularity requirement as $(u,b,θ),$ is regular in $\mathbb{R}^3×(0,T)$ and can be extended as a $C^∞$ solution beyond $T$.

Liangliang Ma. (2021). Conditional Regularity of Weak Solutions to the 3D Magnetic Bénard Fluid System. Journal of Partial Differential Equations. 34 (2). 144-169. doi:10.4208/jpde.v34.n2.4
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