Regularity criterion for a weak solution to the three-dimensional magneto-micropolar fluid equations

摘要

In this paper, a regularity criterion for the 3D magneto-micropolar fluid equations is investigated. A sufficient condition on the derivative of the velocity field in one direction is obtained. More precisely, we prove that if u x 3 belongs to L β ( 0 , T ; L α ( R 3 ) ) with 3 α + 2 β ≤ 1 and α ≥ 3 , then the solution ( u , v , b ) is regular. MSC: 35K15, 35K45.