open access

https://doi.org/10.14943/84103

https://hdl.handle.net/2115/69763

On vorticity directions near singularities for the Navier-Stokes ows with infinite energy

英語

2010-04-12

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

956

1-18

We give a geometric nonblow up criterion on the direction of the vorticity for the three dimensional Navier-Stokes flow whose initial data is just bounded and may have infinite energy. We prove that under a restriction on behavior in time (type I condition) the solution does not blow up if the vorticity direction is uniformly continuous at place where vorticity is large. This improves the Lipschitz regularity condition for the vorticity direction first introduced by P. Constantin and C. Fefferman (1993) for finite energy (weak) solution. Our method is based on a simple blow up argument which says that the situation looks like two-dimensional under continuity of the vorticity direction. We also discuss about boundary value problems.

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