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The steady Navier-Stokes problem for low Reynolds' number viscous jets

The classical existence theorem for the steady Navier-Stokes equations, based on a bound for the solution's Dirichlet integral, provides little qualitative information about the solution.
In particular, if a domain is unbounded, it is not evident that the solution will be unique even when the data are small. Inspired by the works of Odqvist for the interior problem and of Finn for the problem of flow past an obstacle, we give a potential theoretic construction of a solution of the steady Navier-Stokes equations in several domains with noncompact boundaries. We begin by studying a scalar quasilinear elliptic problem in a half space, which serves as a model problem for the development of some of the methods which are later applied to the Navier-Stokes equations. Then, we consider Navier-Stokes flow in a half space, modeling such phenomena as a jet emanating from a wall, with prescribed
boundary values. The solution which is obtained decays like |x|⁻² at infinity and has a finite Dirichlet integral. Finally, we solve the problem of flow through an aperture in a wall between two half spaces, with a prescribed net flux through the aperture, or with a prescribed pressure drop between the two half spaces. A steady solution is constructed which decays like |x|⁻² at infinity. For small data, uniqueness is proven within the class of functions which decay like |x|⁻¹ at infinity and have finite Dirichlet integrals. / Science, Faculty of / Mathematics, Department of / Graduate

Identiferoai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/30968
Date January 1991
CreatorsChang, Huakang
PublisherUniversity of British Columbia
Source SetsUniversity of British Columbia
LanguageEnglish
Detected LanguageEnglish
TypeText, Thesis/Dissertation
RightsFor non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

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