The non-steady Navier-Stokes systems with mixed boundary conditions including friction conditions (Q1782012)

The authors study the non-steady Navier-Stokes and Stokes equations with mixed boundary conditions. The variational inequalities are deduced from the variational formulations in which the mixed boundary conditions are reflected, which are equivalent to the original PDE for smooth solutions. The authors show the existence and uniqueness of the solution to the variational inequality, which implies the similar results for non-steady Navier-Stokes and Stokes equations with mixed boundary conditions. These results extend known one.