Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations

الملخص EN

Regularity criterion for the 3D micropolar fluid equations is investigated.

We prove that, for some T>0, if ∫0T∥vx3∥Lϱρdt<∞, where 3/ϱ+2/ρ≤1 and ϱ≥3, then the solution (v,w) can be extended smoothly beyond t=T.

The derivative vx3 can be substituted with any directional derivative of v.