The role of the pressure in the regularity theory for the Navier-Stokes equations

2021/04/07 by Kwon, Hyunju · 2 citations
#35D30 #76D03 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.03160

Abstract

We first show the equivalence of two classes of generalized suitable weak solutions to the 3D incompressible Navier-Stokes equations allowing distributional pressure, the class of dissipative weak solutions and local suitable weak solutions. Then, an ε-regularity criterion for dissipative weak solutions follows from that for local suitable weak solutions. We relax the ε-regularity criterion with a new approach using a local version of Leray projection operator. As an application of the approach, we obtain the short-time regularity result on a bounded domain for dissipative solutions.

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• Time asymptotics, time regularity and separation rates for Navier-Stokes flows in supercritical solution classes
• The structure of weak solutions to the Navier-Stokes equations

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