Journal article
Nonlinear artificial boundary conditions for the NavierStokes equations in an aperture domain
Publication Details
Authors:  Nazarov, S.; SpecoviusNeugebauer, M.; Videman, J.

Journal:  Mathematical News / Mathematische Nachrichten 
Abstract
We consider the Dirichlet problem for the stationary NavierStokes system in a plane domain Omega, with two angular outlets to infinity. It is known that, under appropriate decay and smallness assumptions, this problem admits solutions with main asymptotic terms in JeffreyHamel form. We will approach these solutions by constructing an approximating problem in the domain Omega(R), which is the intersection of Omega with a sufficiently large circle. The main difficulty, in contrast to the corresponding linear problem, arises from the fact that the main asymptotic term is not known explicitly. Here, we create nonlinear, but local, artificial boundary conditions which involve second order differential operators on the truncation arcs. Unlike for the analogous threedimensional exterior problem, we are able to show the existence of weak solutions to the approximating problem without smoothness nor smallness assumptions. For small data, we prove that the solutions of the approximating problem are unique and regular. Finally, we reach the main goal of this work, i.e. we obtain error estimates in weighted Holder spaces which are asymptotically precise as R tends to infinity. (C) 2004 WILEYVCH Verlag GmbH & Co. KGaA, Weinheim.