Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in ℜ n
Source: Czechoslovak Mathematical Journal, Volume 59, Number 1, March 2009 , pp. 61-79(19)
Abstract:For a bounded domain Ω ⊂ ℜ n , n 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 − Δu + u · ∇u + ∇p = f, div u = k, u |aΩ = g with u ∈ L q , q 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.
Document Type: Research article
Affiliations: 1: Fachbereich Mathematik, Technische Universität Darmstadt, D-642 83, Darmstadt, Germany, Email: email@example.com 2: Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, D-330 98, Paderborn, Germany, Email: firstname.lastname@example.org
Publication date: 2009-03-01