On blowup of nonendpoint borderline Lorentz norms for the Navier-Stokes equations

Abstract

Assuming $T$ is a potential blow up time for the Navier-Stokes system in ${\mathbb{R}}^3$ or ${\mathbb{R}}_{+}^3$, we show that the $L^{3,q}$ Lorentz norm, with $q$ finite, of the velocity field goes to infinity as time $t$ approaches $T$.

15 pages

References in corpus (3)

• Blow-up of critical Besov norms at a potential Navier-Stokes singularity
• A necessary condition of possible blowup for the Navier-Stokes system in half-space
• Blow-up of critical norms for the 3-D Navier-Stokes equations

Cited by in corpus (1)

• On global solutions to the Navier-Stokes system with large $L^{3,\infty }$ initial data