On the existence, uniqueness and regularity of the exterior Stokes problem in \(R^ 3\). (English) Zbl 0608.35056

Guirguis, Georges H.

Commun. Partial Differ. Equations 11, 567-594 (1986).

An analysis is given for a solution to the steady Stokes flow problem on an exterior domain in \({\mathbb{R}}^ 3\). Questions are studied of existence, uniqueness and regularity by using variational methods. By working in weighted function spaces the writer is able to work with a Hilbert space structure which will be useful for finite element construction of solutions.

Reviewer: B.Straugham

MSC:

35Q30	Navier-Stokes equations
35A15	Variational methods applied to PDEs
35B65	Smoothness and regularity of solutions to PDEs
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35Q99	Partial differential equations of mathematical physics and other areas of application

Keywords:

steady Stokes flow; existence; uniqueness; regularity; variational methods; weighted function spaces; Hilbert space; finite element construction

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