On regularity and singularity for L∞(0 , T; L3,w(R3)) solutions to the Navier–Stokes equations

Abstract

We study local regularity properties of a weak solution u to the Cauchy problem of the incompressible Navier–Stokes equations. We present a new regularity criterion for the weak solution u satisfying the condition L∞(0 , T; L3,w(R3)) without any smallness assumption on that scale, where L3,w(R3) denotes the standard weak Lebesgue space. As an application, we conclude that there are at most a finite number of blowup points at any singular time t. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.