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arXiv · 1805.04841

On Wolf's regularity criterion of suitable weak solutions to the Navier-Stokes equations

Quansen Jiu·Yanqing Wang·Daoguo Zhou
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Abstract

In this paper, we consider the local regularity of suitable weak solutions to the 3D incompressible Navier-Stokes equations. By means of the local pressure projection introduced by Wolf in [15,16], we present a $\varepsilon$-regularity criterion below of suitable weak solutions $$ \iint_{Q(1)}|u|^{20/7}dxdt\leq \varepsilon, $$ which gives an improvement of previous corresponding results obtained in Chae and Wolf [3, Arch. Ration. Mech. Anal., 225: 549-572, 2017], in Guevara and Phuc [6, Calc. Var., 56:68, 2017] and in Wolf [16, Ann. Univ. Ferrara, 61: 149-171, 2015].

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Quansen Jiu, Yanqing Wang, Daoguo Zhou. 2018-05-13. On Wolf's regularity criterion of suitable weak solutions to the Navier-Stokes equations. https://doi.org/10.1007/s00021-019-0426-5

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