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 language | English (US) |
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Pages (from-to) | 221-257 |
Number of pages | 37 |
Journal | Communications in Analysis and Geometry |
Volume | 7 |
Issue number | 2 |
DOIs | |
State | Published - Apr 1999 |
All Science Journal Classification (ASJC) codes
- Analysis
- Statistics and Probability
- Geometry and Topology
- Statistics, Probability and Uncertainty