Asymptotics of solutions to the Navier–Stokes system with nonzero flux in a layer-like domain

Article type: Research Article

Authors: Pileckas, K. | Specovius-Neugebauer, M.

Affiliations: Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, Vilnius, 2006 Lithuania. E-mail: [email protected] | Fachbereich 17 Mathematik, Universität Kassel, Heinrich Plett Str. 40, D-34132 Kassel, Germany. E-mail: [email protected] URL: http://www.mathematik.uni-kassel.de/~specovi/

Abstract: The asymptotic behavior in a layer-like domain of weak solutions with nonzero fluxes for the Dirichlet problem of the stationary Navier–Stokes system is investigated. If the data decay sufficiently fast, then first three asymptotic terms of any solution which grows at infinity not “too fast” have the same structure as those for the linear Stokes problem. The first asymptotic term which occurs due to the nonlinearity is of order |x|−3 at infinity in the velocity part; it is constructed explicitly. The results are obtained without any assumption on the smallness of the data.

Keywords: Navier–Stokes system, layer-like domains, asymptotics at infinity

DOI: 10.3233/ASY-2010-1000

Journal: Asymptotic Analysis, vol. 69, no. 3-4, pp. 219-231, 2010