Local Regularity Criteria in Terms of One Velocity Component for the Navier–Stokes Equations

Kyungkeun Kang; Dinh Duong Nguyen

doi:10.1007/s00021-022-00754-8

Local Regularity Criteria in Terms of One Velocity Component for the Navier–Stokes Equations

Kyungkeun Kang, Dinh Duong Nguyen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 LtpLxq-norm of some quantities related to the velocity field is finite and the scaled LtpLxq-norm of one velocity component is sufficiently small near z.

Original language	English
Article number	10
Journal	Journal of Mathematical Fluid Mechanics
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/s00021-022-00754-8
Publication status	Published - 2023 Feb

Bibliographical note

Funding Information:
K. Kang was supported by NRF-2019R1A2C1084685. D. D. Nguyen was supported by NRF-2015R1A5A1009350.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

All Science Journal Classification (ASJC) codes

Mathematical Physics
Condensed Matter Physics
Computational Mathematics
Applied Mathematics

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10.1007/s00021-022-00754-8

Cite this

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Local Regularity Criteria in Terms of One Velocity Component for the Navier–Stokes Equations

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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