# A variational approach to the Navier-Stokes equations

created by gigli on 24 May 2011
modified on 02 Mar 2012

[BibTeX]

Accepted at Bullettin des Sciences Mathematiques

Inserted: 24 may 2011
Last Updated: 2 mar 2012

Year: 2011

Abstract:

We propose a time discretization approach to the Navier-Stokes equations inspired by the theory of gradient flows. This discretization produces LerayHopf solutions in any dimension and suitable solutions in dimension 3. We also show that in dimension 3 and for initial datum in $H^1$, the scheme converges to strong solutions in some interval $[0,T)$ and, if the datum satisfies the classical smallness condition, it produces the smooth solution in $[0,\infty)$.

Keywords: Navier-Stokes, Gradient Flow