# Article

 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 . Category: math . 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 . Date available: 2010-07-20T14:52:56Z Last updated: 2016-04-07 Stable URL: http://hdl.handle.net/10338.dmlcz/140464 . Reference: [1] Adams, R. A.: Sobolev Spaces.Academic Press, New York (1975). Zbl 0314.46030, MR 0450957 Reference: [2] Amann, H.: Nonhomogeneous Navier-Stokes equations with integrable low-regularity data.Int. Math. Ser., Kluwer Academic/Plenum Publishing, New York (2002), 1-28. 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