vii, 159 leaves : ill., graphs, tables ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1979

Thesis (Ph. D.)--University of Sydney, 2000. / Title from title screen (viewed Apr. 23, 2008). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the Dept. of Mechanical Engineering, Faculty of Engineering. Includes bibliography. Also available in print form.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 139-151). Also available via the Internet.

Thesis (Ph. D.)--University of Washington, 1993. / Vita. Includes bibliographical references (leaves [106]-110).

Thesis (M.S.)--University of Toledo, 2010. / Typescript. "Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science degree in Mechanical Engineering." "A thesis entitled"--at head of title. Title from title page of PDF document. Bibliography: p. 51-56.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 92-101). Also available in electronic version.

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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

Many interesting problems in classical physics involve the behavior of solutions of nonlinear hyperbolic systems as certain parameter and coefficients becomes infinite. Quite often, the limiting solution (when it exits) satisfies a completely different nonlinear partial differential equation. The incompressible limit of the compressible Navier-Stokes equations is one physical problem involving dissipation when such a singular limiting process is interesting. In this article we study the time-discretized compressible Navier-Stokes equation and consider the incompressible limit as the Mach number tends to zero. For γ-law gas, 1 < γ ≤ 2, D ≤ 4, we show that the solutions (ρ(ε), μ(ε)/ε) of the compressible Navier-Stokes system converge to the solution (1, v) of the incompressible Navier-Stokes system. Furthermore we also prove that the limit also satisfies the Leray energy inequality.

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