Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary |
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| Authors: | Stephen Gustafson Tai-Peng Tsai |
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| Affiliation: | a Department of Mathematics, The University of British Columbia, Vancouver, BC, Canada V6T 1Z2
b Department of Mathematics, Sungkyunkwan University and Institute of Basic Science, Suwon 440-746, Republic of Korea |
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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  with 3/p+2/q?2, 2<q?∞, (p,q)≠(3/2,∞) 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 additional integral conditions. |
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| Keywords: | Boundary regularity Suitable weak solution Navier-Stokes equations |
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