## Differential and Integral Equations

### The nonlinear Hodge-Navier-Stokes equations in Lipschitz domains

#### Abstract

We investigate the Navier-Stokes equations in a suitable functional setting, in a three-dimensional bounded Lipschitz domain $\Omega$, 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.

#### Article information

Source
Differential Integral Equations Volume 22, Number 3/4 (2009), 339-356.

Dates
First available in Project Euclid: 20 December 2012