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arXiv · 2206.02490

Local regularity criteria in terms of one velocity component for the Navier-Stokes equations

Kyungkeun Kang·Dinh Duong Nguyen
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Abstract

This paper is devoted to presenting new interior regularity criteria in terms of one velocity component for weak solutions to the Navier-Stokes equations in three dimensions. It is shown that the velocity is regular near a point $z$ if its scaled $L^p_tL^q_x$-norm of some quantities related to the velocity field is finite and the scaled $L^p_tL^q_x$-norm of one velocity component is sufficiently small near $z$.

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Kyungkeun Kang, Dinh Duong Nguyen. 2022-06-06. Local regularity criteria in terms of one velocity component for the Navier-Stokes equations. https://doi.org/10.1007/s00021-022-00754-8

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