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LOCAL REGULARITY CRITERIA OF THE NAVIER-STOKES EQUATIONS WITH SLIP BOUNDARY CONDITIONS

  • Bae, Hyeong-Ohk ;
  • Kang, Kyungkeun ;
  • Kim, Myeonghyeon
  • Received : 2015.03.22
  • Published : 2016.05.01

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

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