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Title: Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in $\Bbb R^n$ (English)
Author: Farwig, R.
Author: Sohr, H.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 59
Issue: 1
Year: 2009
Pages: 61-79
Summary lang: English
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Category: math
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Summary: For a bounded domain $\Omega \subset \Bbb R ^n$, $n\geq 3,$ we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system $-\Delta u + u \cdot \nabla u + \nabla p=f$, $\div u = k$, $u_{|_{\partial \Omega }}=g$ with $u \in L^q$, $q \geq n$, and very general data classes for $f$, $k$, $g$ such that $u$ may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of papers by Frehse & Růžička, see e.g. Existence of regular solutions to the stationary Navier-Stokes equations, Math. Ann. 302 (1995), 669--717, where the existence of a weak solution which is locally regular is proved. (English)
Keyword: stationary Stokes and Navier-Stokes system
Keyword: very weak solutions
Keyword: existence and uniqueness in higher dimensions
Keyword: regularity classes in higher dimensions
MSC: 35B65
MSC: 35J55
MSC: 35J65
MSC: 35Q30
MSC: 76D05
MSC: 76D07
idZBL: Zbl 1224.76034
idMR: MR2486616
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Date available: 2010-07-20T14:52:56Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/140464
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