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 - <p style="text-align: justify;">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 $T$.</p>