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

다국어 초록 (Multilingual 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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