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

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


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
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[1] Adams R. A., Sobolev Spaces (1975)
[2] Brezzi F., RAIRO, Series Analyse Numérique 8 pp 129– (1974)
[3] DOI: 10.1007/BF00276169 · Zbl 0096.41303 · doi:10.1007/BF00276169
[4] DOI: 10.1007/BF00297998 · Zbl 0079.12104 · doi:10.1007/BF00297998
[5] Raviart P., Lecture Notes in Mathematics Finite Element Approximations of the Navier-stokes Equations 749 (1979)
[6] Hanouzet A., Rena. Semin. Mat. Univ. Padova 46 pp 227– (1971)
[7] Hardy G., Inequalities · Zbl 0011.15402 · doi:10.1007/BF01218837
[8] The Mathematical Theory of Viscous Incompressible Flow (1969) · Zbl 0184.52603
[9] Necas J., Les Méthodes Directes en Théorie des Equations El Iiptiques (1967)
[10] Nedelec J., Une méthode varitionnelle delements finis pour la resolution3 numérique d’un probleme extérieur dans R 7 pp 105– (1973)
[11] Temam R., Navier-Stokes Equations (1979)
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