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

Hyunju Kwon

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arXiv · 2104.03160

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

Hyunju Kwon

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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 $\varepsilon$-regularity criterion for dissipative weak solutions follows from that for local suitable weak solutions. We relax the $\varepsilon$-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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Hyunju Kwon. 2021-04-07. The role of the pressure in the regularity theory for the Navier-Stokes equations. https://arxiv.org/abs/2104.03160

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