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arXiv math/0505190math.AP
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Navier-斯托克斯方程在边界附近弱解的正则性准则

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

Stephen Gustafson, Kyungkeun Kang, Tai-Peng Tsai

摘要:

本文给出了三维Navier-斯托克斯方程在边界附近"适当弱解“的一些新的正则性准则。我们证明了适当的弱解是Hölder连续的边界,只要尺度混合范数$L^{p,q}_{x,t}$与$3/p+2/q\leq 2, 2<q\le \infty$,$(p,q) \not = (3/2,\infty)$,是小的边界附近。我们的方法在内部情况下也产生了新的结果。在某些Prodi-Serrin型条件下,分析了弱解的部分正则性.

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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