On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space

In this paper the regularity of weak solutions and blow-up criteria for smooth solutions to the micropolar fluid equations in three dimensional space are studied in the Lorentz space L p , ∞ ( R 3 ) Lp,∞(R^3) . We obtain that if u ∈ L q ( 0 , T ; L p , ∞ ( R 3 ) ) u∈ L^q(0,T;Lp,∞(R^3)) for 2 q + 3 p ≤ 1 2q+ 3p≤ 1 with 3 > p ≤ ∞ 3>p≤ ∞ or if ∇ u ∈ L q ( 0 , T ; L p , ∞ ( R 3 ) ) ∇ u∈ L^q(0,T;Lp,∞(R^3)) for 2 q + 3 p ≤ 2 <mml:annotation encoding="applic