A Refinement of the Local Serrin--Type Regularity A refinement of the local Serrin--type regularity criterion for a suitable weak solution to the Navier--Stokes equations

Abstract

We formulate a new criterion for regularity of a suitable weak solution v to the Navier-Stokes equations at the space-time point (x_0,t_0). The criterion imposes a Serrin-type integrability condition on v only in a backward neighbourhood of (x_0,t_0), intersected with the exterior of a certain space-time paraboloid with vertex at point (x_0,t_0). We make no special assumptions on the solution in the interior of the paraboloid.

References in corpus (1)

• A lower bound for the principal eigenvalue of the Stokes operator in a random domain

Cited by in corpus (1)

• A Review of results on axially symmetric Navier-Stokes equations, with addendum by X. Pan and Q. S. Zhang