Local solutions to the Navier-Stokes equations with mixed boundary conditions (Q1281450)

The authors prove the existence and uniqueness of solutions of the three-dimensional Navier-Stokes equations and the continuity equation for homogeneous incompressible fluid with mixed boundary conditions. They also formally derive and then give precisely the weak formulation of the Navier-Stokes system. Finally, they prove the existence and uniqueness of solutions of the Navier-Stokes equations on a time interval in general Lipschitz domains and for a wide class of initial conditions. All proofs are based on the method of functional analysis. This is an interesting mathematical work.