Various boundary conditions for Navier-Stokes equations in bounded Lipschitz domains

Abstract

We present here different boundary conditions for the Navier- Stokes equations in bounded Lipschitz domains in ℝ3, such as Dirichlet, Neumann or Hodge boundary conditions. We first study the linear Stokes operator associated to the boundary conditions. Then we show how the properties of the operator lead to local solutions or global solutions for small initial data.