A variational approach to the Navier-Stokes equations

Nicola Gigli (1) , Sunra Mosconi (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 DMI - Dipartimento di Matematica e Informatica

We propose a time discretization of the Navier-Stokes equations inspired by the theory of gradient flows. This discretization produces Leray/Hopf solutions in any dimension and suitable solutions in dimension 3. We also show that in dimension 3 and for initial datum in H1, 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).

Domaines: Analyse classique [math.CA]

Nicola Gigli, Sunra Mosconi. A variational approach to the Navier-Stokes equations. Bulletin des Sciences Mathématiques, 2012, pp.1-21. ⟨hal-00769387⟩