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Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary

Stephen Gustafson·Kyungkeun Kang·Tai-Peng Tsai
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Abstract

We present some new regularity criteria for ``suitable weak solutions'' of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are Hölder continuous up to the boundary provided that the scaled mixed norm $L^{p,q}_{x,t}$ with $3/p+2/q\leq 2, 2<q\le \infty$, $(p,q) \not = (3/2,\infty)$, is small near the boundary. Our methods yield new results in the interior case as well. Partial regularity of weak solutions is also analyzed under some conditions of the Prodi-Serrin type.

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Stephen Gustafson, Kyungkeun Kang, Tai-Peng Tsai. 2005-05-10. Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary. https://arxiv.org/abs/math/0505190

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