### 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 |
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Pages (from-to) | 161-176 |

Number of pages | 16 |

Journal | Communications in Mathematical Physics |

Volume | 273 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 Jul 1 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*273*(1), 161-176. https://doi.org/10.1007/s00220-007-0214-6

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*Communications in Mathematical Physics*, vol. 273, no. 1, pp. 161-176. https://doi.org/10.1007/s00220-007-0214-6

**Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations.** / Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai Peng.

Research output: Contribution to journal › Article

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 - 2007/7/1

Y1 - 2007/7/1

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 -