Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations

Authors:	Stephen Gustafson Kyungkeun Kang Tai-Peng Tsai

Affiliation:	(1) Department of Mathematics, University of British Columbia, Vancouver, BC, Canada, V6T 1Z2;(2) Department of Mathematics, Sungkyunkwan University and Institute of Basic Science, Suwon, 440-746, Republic of Korea

Abstract:	We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point z if either the scaled ${L^{p,q}_{x,t}}$ -norm of the velocity with 3/p + 2/q ≤ 2, 1 ≤ q ≤ ∞, or the ${L^{p,q}_{x,t}}$ -norm of the vorticity with 3/p + 2/q ≤ 3, 1 ≤ q < ∞, or the ${L^{p,q}_{x,t}}$ -norm of the gradient of the vorticity with 3/p + 2/q ≤ 4, 1 ≤ q, 1 ≤ p, is sufficiently small near z.

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