Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

Stephen Gustafson; Kyungkeun Kang; Tai Peng Tsai

doi:10.1007/s00220-007-0214-6

Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

Stephen Gustafson, Kyungkeun Kang, Tai Peng Tsai

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

59 Citations (Scopus)

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.

Original language	English
Pages (from-to)	161-176
Number of pages	16
Journal	Communications in Mathematical Physics
Volume	273
Issue number	1
DOIs	https://doi.org/10.1007/s00220-007-0214-6
Publication status	Published - 2007 Jul

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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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 Lp,qx,t -norm of the velocity with 3/p+2/q ≤ 2, 1 ≤ q ≤ ∞, or the L p,qx,t-norm of the vorticity with 3/p+2/q ≤ 3, 1 ≤ q < ∞, or the Lp,qx,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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AB - 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 Lp,qx,t -norm of the velocity with 3/p+2/q ≤ 2, 1 ≤ q ≤ ∞, or the L p,qx,t-norm of the vorticity with 3/p+2/q ≤ 3, 1 ≤ q < ∞, or the Lp,qx,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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