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 $T$.