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

Abstract

We study the incompressible magneto-micropolar fluid equations with partial viscosity in R n n 2, 3 . A blow-up criterion of smooth solutions is obtained. The result is analogous to the celebrated Beale-Kato-Majda type criterion for the inviscid Euler equations of incompressible fluids.

Blow-up criterion of smooth solutions for magneto-micropolar fluid equations with partial viscosity

“…We obtain a blow-up criterion of smooth solutions to (1.2), which improves our previous result (see [2]). …”

“…μ, c, g, and ν are constants associated with properties of the material: μ is the kinematic viscosity, c is the vortex viscosity, g and are spin viscosities, and 1 ν is the magnetic Reynold. The incompressible magneto-micropolar fluid equations (1.1) has been studied extensively (see [1][2][3][4][5][6][7][8]). Rojas-Medar [5] established the local in time existence and uniqueness of strong solutions by the spectral Galerkin method.…”

“…Rojas-Medar and Boldrini [6] proved the existence of weak solutions by the Galerkin method, and in 2D case, also proved the uniqueness of the weak solutions. Wang et al [2] obtained a Beale-Kato-Majda type blow-up criterion for smooth solution (u, v, b) to the magneto-micropolar fluid equations with partial viscosity that relies on the vorticity of velocity ∇ × u only (see also [8]). For regularity results, refer to Yuan [7] and Gala [1].…”