Regularity of Leray-Hopf solutions to Navier-Stokes equations (I)-Critical interior regularity in weak spaces

TL;DR

This paper proves interior regularity of Leray-Hopf solutions to Navier-Stokes equations in a critical weak space, solving an open problem and advancing understanding of solution smoothness under minimal regularity assumptions.

Contribution

It establishes interior regularity of Leray-Hopf solutions in the critical space L^2_w(0,T;L^ abla(R^3)), addressing an open problem in the field.

Findings

Proves interior regularity in the critical weak space for Leray-Hopf solutions.

Solves an open problem regarding regularity criteria in weak spaces.

Advances understanding of Navier-Stokes solutions under minimal regularity conditions.

Abstract

We consider the interior regularity of Leray-Hopf solutions to Navier-Stokes equations on critical case L^2_w(0,T;L^\infty(R^3)). Particularly, an open problem proposed in [KK] was solved.