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

62 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

Access to Document

10.1007/s00220-007-0214-6

Cite this

@article{6223ca4bccfe474899e451b383e3df03,

title = "Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations",

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.",

author = "Stephen Gustafson and Kyungkeun Kang and Tsai, {Tai Peng}",

year = "2007",

month = jul,

doi = "10.1007/s00220-007-0214-6",

language = "English",

volume = "273",

pages = "161--176",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

AU - Gustafson, Stephen

AU - Kang, Kyungkeun

AU - Tsai, Tai Peng

PY - 2007/7

Y1 - 2007/7

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=34248574032&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34248574032&partnerID=8YFLogxK

U2 - 10.1007/s00220-007-0214-6

DO - 10.1007/s00220-007-0214-6

M3 - Article

AN - SCOPUS:34248574032

VL - 273

SP - 161

EP - 176

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this