Gradient estimation on Navier-Stokes equations

Gang Tian, Xin Zhouping

Research output: Contribution to journalArticle

66 Scopus citations

Abstract

In this note, we present a prior uniform gradient estimates on solutions to the 3-dimensional Navier-Stokes equations. It is shown that the gradient of the velocity field is locally uniformly bounded in L-norm provided that either the scaled local L2-norm of the vorticity or the scaled local total energy is small. In particular, our results imply that the smooth solutions to 3-dimensional Navier-Stokes equations cannot develop finite time singularity and suitable weak solutions are in fact regular if either the scaled local L2-norm of the vorticity or the scaled local energy is small.

Original languageEnglish (US)
Pages (from-to)221-257
Number of pages37
JournalCommunications in Analysis and Geometry
Volume7
Issue number2
DOIs
StatePublished - Apr 1999

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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