ON THE REGULARITY CRITERION ON ONE VELOCITY COMPONENT FOR THE MICROPOLAR FLUID EQUATIONS

Global Regularity Criterion for the Magneto-Micropolar Fluid Equations

ω(t, x) ∈ Rand b(t, x) ∈ R, and p(t, x) ∈ R denote, respectively, the microrotational velocity, the magnetic field, and the hydrostatic pressure. μ, χ, κ, γ, and ] are positive numbers associated with properties of the material: μ is the kinematic viscosity, χ is the vortex viscosity, κ and γ are spin viscosities, and 1/] is the magnetic Reynold. u 0 , ω 0 , and b 0 are initial data for the vel...

Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations

A Regularity Criterion for the Magneto - Micropolar Fluid Equations in ̇B − 1 ∞ , ∞

Zhihao Tang, GangWang, and Haiwa Guan 1 Department of Fundamentals, Henan Polytechnic Institute, Nanyang, Henan 473009, China 2 Shandong Transport Vocational College, Weifang, Shandong 261206, China 3Department of Public Teaching, Wenzhou Vocational College of Science and Technology, Wenzhou, Zhejiang 325000, China Correspondence should be addressed to Haiwa Guan; [email protected] Received...

A Regularity Criterion for the Angular Velocity Component in Axisymmetric Navier-stokes Equations

We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axisymmetric. We extend the regularity criterion for axisymmetric weak solutions given in [10].

On the regularity criteria of weak solutions to the micropolar fluid equations in Lorentz space

In this paper the regularity of weak solutions and the blow-up criteria of smooth solutions to the micropolar fluid equations on three dimension space are studied in the Lorentz space L(R). We obtain that if u ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 1 with 3 < p ≤ ∞; or ∇u ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 2 with 3 2 < p ≤ ∞; or the pressure P ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 2 with 3 2 < p ≤ ∞; or ∇P ...