Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2016; 53(3): 597-621

Printed May 1, 2016

https://doi.org/10.4134/JKMS.j150191

Copyright © The Korean Mathematical Society.

Local regularity criteria of the Navier-Stokes equations with slip boundary conditions

Hyeong-Ohk Bae, Kyungkeun Kang, and Myeonghyeon Kim

Ajou University, Yonsei University, Yonsei University

Abstract

We present regularity conditions for suitable weak solutions of the Navier-Stokes equations with slip boundary data near the curved boundary. To be more precise, we prove that suitable weak solutions become regular in a neighborhood boundary points, provided the scaled mixed norm $L^{p,q}_{x,t}$ with $3/p+2/q=2$, $1\leq q<\infty$ is sufficiently small in the neighborhood.

Keywords: Navier-Stokes equations, slip boundary data, suitable weak solution

MSC numbers: Primary 35D30, 35Q30