Mathematics – Analysis of PDEs
Scientific paper
2007-05-16
Mathematics
Analysis of PDEs
6 pages
Scientific paper
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. 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.
Vasseur Alexis
No associations
LandOfFree
Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-141850