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

This paper investigates the three dimensional tropic climate equations with fractional diffusion and nonlinear damping. The global exixtence and unique strong solutions of the tropic climate equations have been build under the assumption that initial data $(u_0,v_0,\theta_0)\in H^1(\R^3)\times H^1(\R^3)\times H^1(\R^3)$ with $\alpha>1, \max(1,\frac{p+4}{2p})<\beta, \gamma<1+\frac{3}{p+1}$ and $p,q > 3$.

In this paper, the authors obtain some new blow up criteria for the smooth solution to the three dimensional magnetic B\’enard equation without thermal diffusion in terms of pressure. We prove that if $\pi\in L^2(0, T; L^{\f3r}(\R^3))$ with $0