Blow-up criteria for the 3D Bénard system in Besov spaces

Abstract

Abstract This paper studies the regularity criteria of weak solutions for Bénard fluid flows in three dimensions. When the velocity field and the temperature belong to some critical Besov spaces on (0,T) $(0,T)$, then the weak solution (u,θ) $(u,\theta )$ can be extended smoothly beyond T.

Keywords

• Bénard system
• Regularity criteria
• Besov spaces
• Weak solution
• Global regularity