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Regularity criterion for 3 D Navier-Stokes equations in terms of the direction of the velocity ∗
| Content Provider | Semantic Scholar |
|---|---|
| Author | April, Alexis Vasseur |
| Copyright Year | 2007 |
| Abstract | In this short note, we give a link between the regularity of the solution u to the 3D Navier-Stokes equation, and the behavior of the direction of the velocity u/|u|. It is shown that the control of div(u/|u|) in a suitable Lpt (L q x) norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. But in this case the condition is not on the vorticity, but on the velocity itself. The proof, based on very standard methods, relies on a straightforward relation between the divergence of the direction of the velocity and the growth of energy along streamlines. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ma.utexas.edu/users/vasseur/preprints/NSdirection2.pdf |
| Alternate Webpage(s) | https://www.ma.utexas.edu/users/vasseur/preprints/NSdirection2.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Emoticon Navier–Stokes equations Velocity (software development) Vergence |
| Content Type | Text |
| Resource Type | Article |
