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

Abstract

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∞-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.