On the interior regularity criterion and the number of singular points to the Navier-Stokes equations

Abstract

We establish some interior regularity criterions of suitable weak solutions for the 3-D Navier-Stokes equations, which allow the vertical part of the velocity to be large under the local scaling invariant norm. As an application, we improve Ladyzhenskaya-Prodi-Serrin's criterion and Escauriza-Seregin-Šverák's criterion. We also show that if weak solution $u$ satisfies $$\Vert u(\cdot ,t){\Vert }_{L^p}\le C(-t{)}^{\frac{3-p}{2p}}$$ for some $3<p<\infty$, then the number of singular points is finite.

23 pages

Cited by in corpus (3)

• On blowup of nonendpoint borderline Lorentz norms for the Navier-Stokes equations
• Local boundary regularity for the Navier-Stokes equations in nonendpoint borderline Lorentz spaces
• Boundary Regularity Criteria for the 6D Steady Navier-Stokes and MHD Equations