ON MIXED PRESSURE-VELOCITY REGULARITY CRITERIA FOR THE 3D MICROPOLAR EQUATIONS IN LORENTZ SPACES

In present paper, inspired by the recently paper [1], we give the mixed pressure-velocity regular criteria in view of Lorentz spaces for weak solutions to 3D micropolar equations in a half space. Precisely, if P/(e^{-|x|^2} + |u|)^θ ∈ L^{p}(0, T; L^{q,∞}(R^{3}_{+})) , p, q < 1; and 2/p + 3/q = 2-θ , 0≤θ≤1, then (u,w) is regular on (0,T].