A new blow up criterion for the 3D magneto-micropolar fluid flows
without magnetic diffusion
Abstract
This note obtains a new regularity criterion for the three-dimensional
magneto-micropolar fluid flows in terms of one velocity component and
the gradient field of the magnetic field, i.e. the weak solution
$(u,\omega,b)$ to the magneto-micropolar fluid flows
can be extended beyond time $t=T$, provided if
$u_3\in
L^{\beta}(0,T;L^{\alpha}({\R}^3))$
with
$\f2{\beta}+\f3{\alpha}\leq\f34+\f1{2\alpha},\alpha>\f{10}3$
and $\nabla b\in
L^\f{4p}{3(p-2)}(0,T;\dot{M}_{p,q}({\R}^3))$
with $1