Regularity criteria for the 3D tropical climate model in Morrey-Campanato space

In this paper we investigate the regularity criterion for the local-in-time smooth solution to the three-dimensional (3D) tropical climate model in the Morrey– Campanato space. It is shown that if u satisfies Z T 0 k∇u(t)k 2 r M˙ 2,3/r ln(ku(t)kL 2 + e) dt < ∞ with 0 < r < 1, then the smooth solution (u, v, θ) can be extended past time T

Serrin-type blowup criterion of three-dimensional nonhomogeneous heat conducting magnetohydrodynamic flows with vacuum

We consider an initial boundary value problem for the nonhomogeneous heat conducting magnetohydrodynamic flows. We show that for the initial density allowing vacuum, the strong solution exists globally if the velocity field satisfies Serrin’s condition. Our method relies upon the delicate energy estimates and regularity properties of Stokes system and elliptic equations

Remark on local boundary regularity condition of a suitable weak solution to the 3D MHD equations

We study a local regularity condition for a suitable weak solution of the magnetohydrodynamics equations in a half space R3 +. More precisely, we prove that a suitable weak solution is Hölder continuous near boundary provided that the quantity lim sup r→0 1 r kukL 2(B x,r) L∞(t−r 2,t) is sufficiently small near the boundary. Furthermore, we briefly add some global regularity criteria of weak solutions to this system

On the existence, uniqueness and regularity of solutions for a class of micropolar fluids with shear dependent viscosities

In this paper we consider a model describing the motion of a class of micropolar fluids with shear-dependent viscosities in a smooth domain Ω ⊂ R2. Under the conditions that the external force and vortex viscosity µr are small in a suitable sense, we proved the existence and uniqueness of regularized solutions for the problem by using the iterative method