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

- 1. 0348177 - MU-W 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

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/11104/0188774File Download Size Commentary Version Access Neustupa4.pdf 8 273.2 KB Publisher’s postprint require