We consider the Navier-Stokes equations with Navier friction boundary conditions and prove two results. First, in the case of a bounded domain we prove that weak Leray solutions converge (locally in time in dimension â‰¥ 3 and globally in time in dimension 2) as the viscosity goes to 0 to a strong solution of the Euler equations provided that the initial dataâ€¦ (More)

In [1], T. Clopeau, A. MikeliÄ‡, and R. Robert studied the inviscid limit of the 2D incompressible Navier-Stokes equations in a bounded domain subject to Navier friction-type boundary conditions. They proved that the inviscid limit satisfies the incompressible Euler equations and their result ultimately includes flows generated by bounded initialâ€¦ (More)

We consider a phase-field model for a phase change process with phase-dependent heat absorption. This model describes the behaviour of films exposed to radiative heating, where the film can change reversibly between amorphous and crystalline states. Existence and uniqueness of solutions as well as stability are established. Moreover, a maximum principle isâ€¦ (More)

In this talk we address the issue of existence of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the convergence, as the viscosity goes to zero, of weak solutions for the non-homogeneous Navier-Stokes systemâ€¦ (More)