A Beale-Kato-Madja Criterion for Magneto-Micropolar Fluid Equations with Partial Viscosity

A Beale-Kato-Madja Criterion for Magneto-Micropolar Fluid Equations with Partial Viscosity

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...

The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations

Here u, b describe the flow velocity vector and the magnetic field vector respectively, p is a scalar pressure, ν > 0 is the kinematic viscosity and η > 0 is the magnetic diffusivity, while u0 and b0 are the given initial velocity and initial magnetic field respectively, with ∇ · u0 = ∇ · b0 = 0. If ν = η = 0, (1.1) is called the ideal MHD equations. Using the standard energy method, it can be ...

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...

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, prove the existence of the strong solution with initial data in H(R) 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, ω, b) which relies on the vorticity of velocity ∇× u only.