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.
Hyeong-Ohk Bae, Kyungkeun Kang, and Myeonghyeon Kim
Ajou University, Yonsei University, Yonsei University
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
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