Open AccessJournal Article
Resolvent estimates of the Stokes system with Navier boundary conditions in general unbounded domains
Reinhard Farwig,Veronika Rosteck +1 more
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In this article, the Stokes resolvent system in general unbounded domains was studied and the main result was that the resolvability estimate in function spaces of the type ${\tilde{L}^q}$ defined as $L^q\cap L^2$ when $q\geq 2$ was adapted to the unboundedness of the domain.Citations
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Journal ArticleDOI
On Critical Spaces for the Navier–Stokes Equations
Jan Prüss,Mathias Wilke +1 more
TL;DR: The abstract theory of critical spaces developed in Pruss and Wilke (J Evol Equ, 2017) is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions as discussed by the authors.
Book ChapterDOI
Stokes semigroups, strong,weak, and very weak solutions for general domains
TL;DR: In this paper, the main properties of the spaces Q L. / and related concepts for solenoidal subspaces, Sobolev spaces, Bochner spaces, and the corresponding Helmholtz projection and Stokes operator are discussed.
Dissertation
Navier-Stokes Equations with Navier Boundary Condition
TL;DR: In this paper, Stokes and Navier Stokes with condiciones de contorno de Navier have been studied. But the result of the convergencia of these results to the results of Dirichlet et al. has not yet been established.
Journal ArticleDOI
Note on Friedrichs' inequality in N-star-shaped domains
Reinhard Farwig,Veronika Rosteck +1 more
TL;DR: In this article, an explicit constant in the Friedrichs inequality for N-star-shaped domains with respect to convex sets was established, which can be generalized to higher order moments when replacing the integral mean of u over S by the mean of higher order Taylor polynomials.
Journal ArticleDOI
Control at a distance of the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid
TL;DR: In this article, the authors consider the case of a rigid body immersed in a viscous incompressible fluid with Navier slip-with-friction conditions at the solid boundary and prove the small-time global exact controllability of the position and velocity of the rigid body when the control takes the form of a distributed force supported in a compact subset of the fluid domain, away from the body.
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