On the inviscid limit of the Navier-Stokes equations for flows with large flux

摘要

We investigate the inviscid limit of solutions of the evolutionary and stationary Navier-Stokes equations in two-dimensional bounded domains. The system is considered with the slip boundary conditions admitting flows across the boundary. Under a geometrical restriction on the shape of the domain, we prove the L-infinity-bound on the vorticity of the velocity for any large boundary data. This estimate enables us to prove the existence of solutions to the Navier-Stokes equations. Moreover the bound is independent of the viscosity and guarantees a strong convergence to the Eulerian limit. The result for the nonsteady case is global in time. [References: 15]