Local stability of energy estimates for the Navier--Stokes equations

TL;DR

This paper investigates the local stability of energy estimates for the Navier--Stokes equations, focusing on the regularity of weak limits of dissipative solutions without pressure assumptions.

Contribution

It provides new insights into the stability and regularity of weak solutions to Navier--Stokes without pressure constraints.

Findings

Establishes conditions for local stability of energy estimates.

Shows regularity of weak limits under minimal pressure assumptions.

Advances understanding of dissipative solutions in fluid dynamics.

Abstract

We study the regularity of the weak limit of a sequence of dissipative solutions to the Navier--Stokes equations when no assumptions is made on the behavior of the pressures.