REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

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In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magueto-micropolar fluid equations in (R)3. We obtain the classical blow-up criteria for smooth solutions (u, w, b), i.e., u ∈ Lq(O,T;LP(R3)) for 2/q+3/p ≤ 1 with 3 < p ≤∞, u ∈ C([O,T);L3(R3)) or ▽u ∈ Lq(O,T;LP) 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 u ∈ L1 (O, T; BO∞,∞(R3)).
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