REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

doi:10.1016/S0252-9602(10)60139-7

Abstract

Abstract:

In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid
equations in R³. We obtain the classical blow-up criteria for smooth solutions (u, ω,b), i.e., L^q(0,T; L^p(R³) )for 2/q+3/p≤1 with 3<p≤∞, u ∈ C([0, T); L³(R³)) or $\nabla u\in L^q(0, T; L^p) for 3/2< p ≤∞ satisfying 2/q+3/p≤2. Moreover, our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid. In the end-point case p=∞, the blow-up criteria can be extended to more general spaces $\nabla u\in L¹(0, T; B⁰_∞,_∞(R³)).

Key words: magneto-micropolar fluid equations, regularity criteria, blow-up criteria

CLC Number:

35Q35

YUAN Bao-Quan. REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS[J].Acta mathematica scientia,Series B, 2010, 30(5): 1469-1480.

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