Regularity results for solutions of micropolar fluid equations in terms of the pressure

This paper is devoted to investigating regularity criteria for the 3D micropolar fluid equations in terms of pressure in weak Lebesgue space. More precisely, we prove that the weak solution is regular on (0, T] provided that either the norm II & pi;IIL & alpha;,& INFIN;(0,T;L & beta;,& INFIN;(R3)) with 2 & alpha; + & beta;3 = 2 and 32 < & beta; < & INFIN; or IIV & pi;IIL & alpha;,& INFIN;(0,T;L & beta;,& INFIN;(R3)) with 2 & alpha; + & beta;3 = 3 and 1 < & beta; < & INFIN; is sufficiently small.

Automated summary

This paper investigates the regularity criteria for the 3D micropolar fluid equations in terms of pressure in weak Lebesgue space. It is proven that the weak solution is regular on (0, T] if the pressure satisfies either the norm IIπIILα,∞(0,T;Lβ,∞(R3)) with 2α+β/3=2 and 32<β<∞ or IIVπIILα,∞(0,T;Lβ,∞(R3)) with 2α+β/3=3 and 1<β<∞ is sufficiently small.