Remarks on Interior Regularity Criteria Without Pressure for the Navier-Stokes Equations

Shuai Li; Wendong Wang; Daoguo Zhou

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arXiv · 2305.00698

Remarks on Interior Regularity Criteria Without Pressure for the Navier-Stokes Equations

Shuai Li·Wendong Wang·Daoguo Zhou

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Abstract

In this note we investigate interior regularity criteria for suitable weak solutions to the 3D Naiver-Stokes equations, and obtain the solutions are regular in the interior if the $L^p_tL_x^q(Q_1)$ norm of the velocity is sufficiently small, where $1\leq \frac{2}{p}+\frac{3}{q}<2$ and $2\leq p\leq \infty$. It improves the recent result of $p,q>2 $ by Kwon \cite{Kwon} (J. Differential Equations 357 (2023), 1--31.), and also generalizes Chae-Wolf's $L_t^\infty L_x^{\frac32+}$ criterion \cite{CW2017} (Arch. Ration. Mech. Anal. 225 (2017), no. 1, 549--572.).

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Shuai Li, Wendong Wang, Daoguo Zhou. 2023-05-01. Remarks on Interior Regularity Criteria Without Pressure for the Navier-Stokes Equations. https://arxiv.org/abs/2305.00698

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