Blow-up criterion for strong solutions to the 3D magneto-micropolar fluid equations in the multiplier space

Abstract

In this article, we study the blow-up of strong solutions to the magneto-micropolar (MMP) fluid equations in $mathbb{R}^3$. It is proved that if the gradient field of velocity satisfies $$ abla uin L^{2/(2-r)}(0,T;dot{X}_r(mathbb{R}^3))quad hbox{with }rin[0,1], $$ then the strong solution $(u,w,b)$ can be extended beyond $t=T$.

Keywords

• Magneto-micropolar equations
• blow-up criterion
• multiplier spaces