A new approach to the existence of weak solutions of the steady Navier-Stokes system with inhomogeneous boundary data in domains with noncompact boundaries

0348177 - MÚ 2011 RIV DE eng J - Journal Article
Neustupa, Jiří
A new approach to the existence of weak solutions of the steady Navier-Stokes system with inhomogeneous boundary data in domains with noncompact boundaries.
Archive for Rational Mechanics and Analysis. Roč. 198, č. 1 (2010), 331-348. ISSN 0003-9527. E-ISSN 1432-0673
R&D Projects: GA ČR GA201/08/0012
Institutional research plan: CEZ:AV0Z10190503
Keywords : Navier-Stokes equations * inhomogeneous boundary data
Subject RIV: BA - General Mathematics
Impact factor: 2.277, year: 2010
http://link.springer.com/article/10.1007%2Fs00205-010-0297-7

We prove the existence of a weak solution to the steady Navier-Stokes problem in a three dimensional domain Omega, whose boundary partial derivative,Omega consists of M unbounded components Gamma(1), . . . ,Gamma(M) and N - M bounded components Gamma(M+1), . . . , Gamma(N) . We use the inhomogeneous Dirichlet boundary condition on partial derivative Omega. The prescribed velocity profile alpha on partial derivative Omega is assumed to have an L-3-extension to Omega with the gradient in L-2(Omega)(3x3). We assume that the fluxes of alpha through the bounded components Gamma(M+1), . . . , Gamma(N) of a,I (c) are "sufficiently small", but we impose no restriction on the size of fluxes through the unbounded components Gamma(1), . . . , Gamma(M).
Permanent Link: http://hdl.handle.net/11104/0188774