2009-07-02Buch DOI: 10.18452/2762
Existence of turbulent weak solutions to the generalized Navier-Stokes equations in exterior domains and large time behaviour
 dc.contributor.author Wolf, Jörg dc.date.accessioned 2017-06-15T18:13:13Z dc.date.available 2017-06-15T18:13:13Z dc.date.created 2009-07-02 dc.date.issued 2009-07-02 dc.identifier.issn 0863-0976 dc.identifier.uri http://edoc.hu-berlin.de/18452/3414 dc.description.abstract Let $\Omega$ be an exterior domain in $\R^n\,(n=2,3,4)$ , with boundary being not necessarily smooth. For any initial velocity ${\bf u}_0\in L^2(\Omega)^n$ such that $\nabla\cdot {\bf u}_0=0$ (in sense of distribution) and external forces $\bfF\in L^1(0,\infty; L^2(\Omega )^n)+ L^2(0,\infty; W^{-1,2} (\Omega )^n)$ we are able to construct a turbulent weak solution ${\bf u}\in C_w([0,\infty); L^2(\Omega)^n)\cap L^2(0,\infty; W^{1, 2}_0(\Omega )^n)$ to the equations of motion of a non-Newtonian fluid. Simultaneously, we prove that this solution fulfils the non-uniform decay condition $\|\bfu(t)\|_{L^2(\Omega)} \rightarrow 0 \quad \mbox{as}\quad t \rightarrow \infty.$ eng dc.language.iso eng dc.publisher Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik dc.subject General fluids eng dc.subject existence of weak solutions eng dc.subject asymptotic behaviour eng dc.subject.ddc 510 Mathematik dc.title Existence of turbulent weak solutions to the generalized Navier-Stokes equations in exterior domains and large time behaviour dc.type book dc.identifier.urn urn:nbn:de:kobv:11-110-18452/3414-9 dc.identifier.doi http://dx.doi.org/10.18452/2762 local.edoc.container-title Preprints aus dem Institut für Mathematik local.edoc.pages 35 local.edoc.type-name Buch local.edoc.container-type series local.edoc.container-type-name Schriftenreihe local.edoc.container-volume 2007 local.edoc.container-issue 4 local.edoc.container-year 2007 local.edoc.container-erstkatid 2075199-0