Regularity criterion for 3d navier-stokes equations in terms of the direction of the velocity |
| |
Authors: | Email author" target="_blank">Alexis?VasseurEmail author |
| |
Institution: | (1) Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257, USA |
| |
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 L
t/p
(L
x/q
) 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. However, 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.
This work was supported in part by NSF Grant DMS-0607953. |
| |
Keywords: | Navier-Stokes fluid mechanics regularity PRodi-Serrin criteria |
本文献已被 SpringerLink 等数据库收录! |
|