Abstract
In this paper, we investigate the Cauchy problem for the incompressible magneto-micropolar fluid equations with partial viscosity in ℝn(n = 2, 3). We obtain a Beale-Kato-Majda type blow-up criterion of smooth solutions.MSC (2010): 76D03; 35Q35.
Highlights
The incompressible magneto-micropolar fluid equations in Rn(n = 2, 3) takes the following form⎧ ⎪⎪⎪⎪⎪⎨ ∂tu − (μ + χ )u + u · ∇u − b · ∇b + ∇(p + 1 |b|2) − χ ∇ × v = 0, 2∂tv − γ v − κ∇divv + 2χ v + u · ∇v − χ ∇ × u = 0, ⎪⎪⎪⎪⎪⎩ ∂t b ∇· −ν u= b 0,+ u · ∇b − ∇ · b = 0, b · ∇u
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
We obtain a blow-up criterion of smooth solutions to (1.2), which improves our previous result
Summary
1 Introduction The incompressible magneto-micropolar fluid equations in Rn(n = 2, 3) takes the following form The incompressible magneto-micropolar fluid equations (1.1) has been studied extensively (see [1,2,3,4,5,6,7,8]). Global existence of strong solution for small initial data was obtained in [4]. 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 [8]).
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