Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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LOCAL REGULARITY CRITERIA OF THE NAVIER-STOKES EQUATIONS WITH SLIP BOUNDARY CONDITIONS

  • Received : 2015.03.22
  • Published : 2016.05.01
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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.

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References

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