Existence theorem and blow-up criterion of the strong solutions to the Magneto-micropolar fluid equations

In this paper we study the magneto-micropolar fluid equations in $\R^3$, prove the existence of the strong solution with initial data in $H^s(\R^3)$ for $s> {3/2}$, and set up its blow-up criterion. The tool we mainly use is Littlewood-Paley decomposition, by which we obtain a Beale-Kato-Majda type blow-up criterion for smooth solution $(u,\omega,b)$ which relies on the vorticity of velocity $\nabla\times u$ only.Comment: 19page

A new regularity criterion of weak solutions to the 3D micropolar fluid flows in terms of the pressure

In this study, we establish a new regularity criterion of weak solutions to the three-dimensional micropolar fluid flows by imposing a critical growth condition on the pressure field. © 2020, Unione Matematica Italiana

A New Pressure Regularity Criterion of the Three-Dimensional Micropolar Fluid Equations

This paper concerns the regularity criterion of the weak solutions to the three-dimensional (3D) micropolar fluid equations in terms of the pressure. It is proved that if one of the partial derivatives of pressure satisfies ∂3π∈Lp(0,T;Lq(R3)) with 2/p+3/q≤2,3<q<∞,1<p<∞, then the weak solution of the micropolar fluid equations becomes regular on (0,T]

A regularity criterion for the three-dimensional micropolar fluid system in homogeneous Besov spaces

By establishing a new trilinear estimate, we show a regularity criterion for the three dimensional micropolar fluid system via the velocity in homogeneous Besov spaces. This improves [B. Q. Dong, Z. L. Zhang, On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces, Nonlinear Anal. 73(2010), 2334-2341] in some sense

Logarithmical Regularity Criteria of the Three-Dimensional Micropolar Fluid Equations in terms of the Pressure

This paper is devoted to the regularity criterion of the three-dimensional micropolar fluid equations. Some new regularity criteria in terms of the partial derivative of the pressure in the Lebesgue spaces and the Besov spaces are obtained which improve the previous results on the micropolar fluid equations

Regularity results for solutions of micropolar fluid equations in terms of the pressure

This paper is devoted to investigating regularity criteria for the 3D micropolar fluid equations in terms of pressure in weak Lebesgue space. More precisely, we prove that the weak solution is regular on $(0, T]$ provided that either the norm $\left\Vert \pi \right\Vert _{L^{\alpha, \infty }(0, T;L^{\beta, \infty }(\mathbb{R}^{3}))}$ with $\frac{2}{\alpha }+ \frac{3}{\beta } = 2$ and \frac{3}{2} < \beta < \infty or $\left\Vert \nabla \pi \right\Vert _{L^{\alpha, \infty }(0, T;L^{\beta, \infty }(\mathbb{R} ^{3}))}$ with $\frac{2}{\alpha }+\frac{3}{\beta } = 3$ and 1 < \beta < \infty is sufficiently small