| Abstract: |
| This talk is concerned with a regularity criterion based on vorticity direction for the three-dimensional Navier-Stokes equations under the no-slip boundary condition. Intuitively speaking, our result says that the type I blow-up does not occur unless vorticity direction is drastically changing depending on space. This kind of a non-blow up criterion based on the vorticity direction was first suggested by P. Constantin and C. Fefferman in the whole space case. Their method is a kind of energy method. We extend the result to several domains under the no-slip boundary condition by proving a Liouville theorem and pressure estimates.
More precisely, it asserts that if the vorticity direction is uniformly continuous in space uniformly in time, there is no type I blow-up for several kind of domains. |
|