ASYMPTOTIC ANALYSIS OF THE NAVIER-STOKES EQUATIONS IN A CURVED DOMAIN WITH A NON-CHARACTERISTIC BOUNDARY

We consider the Navier-Stokes equations of an incompressible fluid in a three dimensional curved domain with permeable walls in the limit of small viscosity. Using a curvilinear coordinate system, adapted to the boundary, we construct a corrector function at order epsilon(j) , j = 0, 1 , where epsilon is the (small) viscosity parameter. This allows us to obtain an asymptotic expansion of the Navier-Stokes solution at order epsilon(j) , j = 0, 1 , for epsilon small . Using the asymptotic expansion, we prove that the Navier-Stokes solutions converge, as the viscosity parameter tends to zero, to the corresponding Euler solution in the natural energy norm. This work generalizes earlier results in [14] or [26], which discussed the case of a channel domain, while here the domain is curved.