Remarks on the Regularity Criterion of the Navier-Stokes Equations with Nonlinear Damping

Abstract EN

This paper is concerned with the regularity criterion of weak solutions to the three-dimensional Navier-Stokes equations with nonlinear damping in critical weak Lq spaces.

It is proved that if the weak solution satisfies ∫0T∇u1Lq,∞2q/2q-3+∇u2Lq,∞2q/2q-3/1+lne+∇uL22ds<∞, q>3/2, then the weak solution of Navier-Stokes equations with nonlinear damping is regular on (0,T].