A weak-Lp Prodi-Serrin type regularity criterion for the micropolar fluid equations

We investigate regularity criteria for weak solutions of the micropolar fluid equations in a bounded three-dimensional domain. We show that the solution (u, w) is strong on [0, T] if either u ∈ Ls (0, T; L r,∞(Ω)) or ‖u‖ L s,∞(0,T;L r,∞(Ω)) is bounded from above by a specific constant, where (3/r) + (2/s) = 1 and r > 3.