Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in $\Bbb R^n$

Title:

Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in $\Bbb R^n$

Creator:

Farwig, Reinhard and Sohr, Hermann

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:52ed7e59-f9dd-45a5-9a73-59d4d41f79ec
uuid:52ed7e59-f9dd-45a5-9a73-59d4d41f79ec

Subject:

stationary Stokes and Navier-Stokes system, very weak solutions;, existence and uniqueness in higher dimensions, and regularity classes in higher dimensions

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

61-79

Source:

Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:1

Harvested from:

CDK

Metadata only:

false