abstract / Mechanical Engineering / Master / Master of Philosophy

Finally, we discuss some open problems closely related to the results obtained in this thesis and give some perspectives. / First, we study global subsonic and subsonic-sonic potential flows through a general infinitely long two dimensional or three dimensional axially symmetric nozzle. It is proved that there exists a critical value for the incoming mass flux so that a global uniformly subsonic flow exists in the nozzle as long as the incoming mass flux is less than the critical value. Furthermore, we establish some uniform estimates for the deflection angles and the minimum speed of the subsonic flows by combining the hodograph transformation and the comparison principle for elliptic equations. With the help of these properties and a compensated compactness framework, we prove the existence of a global subsonic-sonic flow solution in the case of the critical incoming mass flux. / Second, global existence of steady subsonic Euler flows through infinitely long nozzles is established when the variation of Bernoulli's constant in the upstream is sufficiently small and mass flux is in a suitable regime with an upper critical value. One of the main difficulties lies in that the full steady Euler system is a hyperbolic-elliptic coupled system in a subsonic region. A key point is to use stream function formulation for compressible Euler equations. By this formulation, Euler equations are equivalent to a quasilinear second order equation for stream function. We obtain existence of solution to the boundary value problem for stream function with the help of estimate for elliptic equation of two variables. Asymptotic behavior for the stream function is obtained via a blow up argument and energy estimate. This asymptotic behavior, together with some refined estimates on the stream function, yields the consistency of the stream function formulation and the original Euler equations. / Xie, Chunjing. / "August 2007." / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1075. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 139-140). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

本論文會討論有關於二維的耗散準地轉方程，特別是有關於存在性及規律性的問題。有關的討論主要取決於該方程的分數冪。這份論文中將會介紹一些最近有關耗散準地轉方程的結果。 / This paper is discussing about problems in the 2-D Dissipative Quasi-Geostrophic equation, mainly the existence and regularity results, depending on the fractional power. We will introduce the recent results in this topics. / Detailed summary in vernacular field only. / Kwan, Danny. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 65-68). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- Main Results in QG --- p.9 / Chapter 2.1 --- Definitions --- p.9 / Chapter 2.2 --- Subcritical Case (γ>[1/2]) --- p.10 / Chapter 2.3 --- Critical Case (γ=[1/2]) --- p.10 / Chapter 2.4 --- Supercritical Case (γ<[1/2]) --- p.11 / Chapter 3 --- The Proofs of Main Results --- p.12 / Chapter 3.1 --- Some Previous Results --- p.12 / Chapter 3.2 --- Subcritical Case (γ>[1/2]) --- p.14 / Chapter 3.2.1 --- Proof of Theorem 1 --- p.14 / Chapter 3.2.2 --- Proof of Theorem 2 --- p.19 / Chapter 3.2.3 --- Proof of Corollary 1 --- p.25 / Chapter 3.2.4 --- Summary for Subcritical Case --- p.27 / Chapter 3.3 --- Critical Case (γ=[1/2]) --- p.28 / Chapter 3.3.1 --- Proof of Theorem 3 --- p.28 / Chapter 3.3.2 --- Proof of Theorem 4 --- p.36 / Chapter 3.3.3 --- Summary for Critical Case --- p.41 / Chapter 3.4 --- Supercritical Case (γ<[1/2]) --- p.41 / Chapter 3.4.1 --- Proof of Theorem 5 --- p.41 / Chapter 3.4.2 --- Proof of Theorem 6 --- p.50 / Chapter 3.4.3 --- Proof of Theorem 7 --- p.54 / Chapter 3.4.4 --- Summary for Supercritical Case --- p.64 / Chapter 4 --- Further Development --- p.65

Next, we consider that the fluids are isentropic and the domain is also bounded, smooth, simply connected in R2 . We show that the estimates are uniform in all time if the smallness assumption on the initial data is prescribed. It follows that the solutions of compressible Navier-Stokes equations converge to the incompressible ones uniformly in both spatial and temporal variables as the Mach number vanishes. / This thesis deals with the low Mach number limit of the compressible Navier-Stokes equations. It is to verify that the compressible fluids become incompressible as Mach number tends to zero. In another words, the pressure due to compression can be neglected. This is a singular limit. / We will show that, as the Mach number tends to zero, the local smooth solutions of compressible Navier-Stokes equations with zero thermal conductivity coefficient converge strongly to the solutions of incompressible Navier-Stokes equations, provided that the initial data satisfy the "bounded derivative conditions". The key point, which is one of our main contributions, is the uniform high norm estimates in Mach number. We will study two cases. The first case is that, the domain is a finite interval and the boundary condition for the velocity is no-slip. In the second case, the domain is bounded, smooth, and simply connected in R2 . The boundary condition for the velocity is replaced by the slip-type's, thus the vorticity and the divergence of velocity can be estimated separately. / Ou, Yaobin. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3546. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 107-111). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

No description available.

Chu Shun Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 63-65). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.8 / Chapter 2 --- Singular Integrals --- p.15 / Chapter 2.1 --- Marcinkiewicz Integral --- p.15 / Chapter 2.2 --- Decomposition in cubes of open sets in Rn --- p.17 / Chapter 2.3 --- Interpolation Theorem for Lp --- p.18 / Chapter 2.4 --- Singular Integrals on homogeneous of degree 0 --- p.25 / Chapter 3 --- Solutions to the Euler Equations --- p.36 / Chapter 3.1 --- Existence and Uniqueness of smooth solutions for Euler Equations --- p.36 / Chapter 3.2 --- Rate of Convergence and Decay in Time --- p.43 / Chapter 3.2.1 --- Rate of Convergence --- p.43 / Chapter 3.2.2 --- Lp Decay for Solutions of the Navier-Stokes Equations --- p.46 / Chapter 3.3 --- Weak Solution to the Euler Equations --- p.48 / Chapter 3.3.1 --- Weak Solution to the Velocity Formulation --- p.49 / Chapter 3.3.2 --- Weak Solution to the Vorticity Formulation --- p.52 / Bibliography --- p.63

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Bibliography: leaves 77-78 / 78 leaves : ill. (some col.) ; 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, 1986

One approach to examining the stability of a fluid flow is to linearize the evolution equation at an equilibrium and determine (if possible) the stability of the resulting linear evolution equation. In this dissertation, the space of perturbations of the equilibrium flow is split into two classes and growth of the linear evolution operator on each class is analyzed. Our classification of perturbations is most naturally described in V.I. Arnold’s geometric view of fluid dynamics. The first class of perturbations we examine are those that preserve the topology of vortex lines and the second class is the factor space corresponding to the first class. In this dissertation we establish lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbations. / text