THE NONLINEAR HODGE-NAVIER-STOKES EQUATIONS IN LIPSCHITZ DOMAINS

Marius Mitrea (1) , Sylvie Monniaux (2)

1 Department of Mathematics [New York]
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We investigate the Navier-Stokes equations in a suitable functional setting, in a three-dimensional bounded Lipschitz domain, equipped with "free boundary" conditions. In this context, we employ the Fujita-Kato method and prove the existence of a local mild solution. Our approach makes essential use of the properties of the Hodge-Laplacian in Lipschitz domains.

Mots clés: Hodge-Navier-Stokes system; Lipschitz domain; Mild solutions

Domaines: Equations aux dérivées partielles [math.AP]

Marius Mitrea, Sylvie Monniaux. THE NONLINEAR HODGE-NAVIER-STOKES EQUATIONS IN LIPSCHITZ DOMAINS. Differential and integral equations, 2009, 22 (3-4), pp.339-356. ⟨hal-00535704⟩