Finally, we investigate the motion of a general form rigid body with smooth boundary by an incompressible perfect fluid occupying R3 . Due to the domain occupied by the fluid depending on the time, this problem can be transformed into a new systems of the fluid in a fixed domain by the frame attached with the body. With the aid of Kato-Lai's theory, we construct a sequence of successive solutions to this problem in some unform time interval. Then by a fixed point argument, we have proved that the existence, uniqueness and persistence of the regularity for the solutions of original fluid-structure interaction problem. / In the first part, we study the issue of the inviscid limit of the incompressible Navier-Stokes equations on the general smooth domains for completely slip boundary conditions. We verify an asymptotic expansion which involves a weak amplitude boundary layer with the same thickness as in the Prantle's theory. We improve the better regularity for the boundary layer and obtain the uniform Lp--estimates (3 < p ≤ 6) of the remainder. Then we improved these estimates to H 1--estimates. It is shown that the viscous solution converges to the solution of Euler equation in C([0, T]; H1(O)) as the viscosity tends to zero. / In the second part, we consider the non-stationary problems of a class of non-Newtonian fluid which is a power law fluid with p > 3nn+2 in the half space with slip boundary conditions. We present the local pressure estimate with the Navier's slip boundary conditions. Using these estimates and an Linfinity -- truncation method, we can obtain that this system has at least one required weak solution. / In this thesis, we study several issues involving incompressible viscous fluids with the slip boundary conditions and the motions of fluid-solid interactions. / Zang, Aibin. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 128-141). / 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, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Duan, Ben. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 61-67). / Abstracts in English and Chinese. / Acknowledgments --- p.2 / Abstract --- p.i / Introduction --- p.3 / Chapter 1 --- Stability of Shock Waves in Viscous Conservation Laws --- p.10 / Chapter 1.1 --- Cauchy Problem for Scalar Viscous Conservation Laws and Viscous Shock Profiles --- p.10 / Chapter 1.2 --- Stability of Shock Waves by Energy Method --- p.15 / Chapter 1.3 --- L1 Stability of Shock Waves in Scalar Viscous Con- servation Laws --- p.20 / Chapter 2 --- Slow Motion of a Viscous Shock --- p.29 / Chapter 2.1 --- Propagation of a Viscous Shock in Bounded Domain --- p.29 / Chapter 2.1.1 --- Steady Problem --- p.30 / Chapter 2.1.2 --- Time-Dependent Problem --- p.34 / Chapter 2.1.3 --- Super-Sensitivity of Boundary Conditions --- p.36 / Chapter 2.2 --- Propagation of a Stationary Shock in Half Space --- p.39 / Chapter 2.2.1 --- Asymptotic Analysis --- p.39 / Chapter 2.2.2 --- Pointwise Estimate --- p.40 / Chapter 3 --- Viscous Transonic Flow Through a Nozzle --- p.47 / Chapter 3.1 --- Nonlinear Stability and Instability of Shock Waves --- p.48 / Chapter 3.2 --- Asymptotic Stability and Instability --- p.49 / Chapter 3.3 --- Matched Asymptotic Analysis --- p.53 / Chapter 4 --- C --- p.60 / Bibliography --- p.61

Bibliography: leaves 247-257. Electronic publication; Full text available in PDF format; abstract in HTML format. This thesis examines the flow of very viscous Newtonian fluids driven by gravity, with emphasis on the lumping of molten glass into a mould, as in the manufacture of optical components, which are in turn used to manufacture ophthalmic lenses. Electronic reproduction.[Australia] :Australian Digital Theses Program,2001.

Yu, Rongfeng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 57-63). / Abstracts in English and Chinese. / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.11 / Chapter 1.1 --- Notations and function spaces --- p.11 / Chapter 1.2 --- Some useful inequalities --- p.12 / Chapter 1.3 --- Fundamental lemmas --- p.15 / Chapter 2 --- Compressible Navier-Stokes Equations for Quantum Fluids --- p.16 / Chapter 2.1 --- Background --- p.17 / Chapter 2.2 --- Derivation of model --- p.17 / Chapter 3 --- Global Weak Solutions to Barotropic Navier-Stokes Equations for Quantum Fluids --- p.22 / Chapter 3.1 --- Reformulation and main results --- p.23 / Chapter 3.2 --- Construction of approximate solutions --- p.27 / Chapter 3.3 --- A priori estimates --- p.39 / Chapter 3.4 --- Proof of Theorem 3.1.6 --- p.40 / Chapter 4 --- Global Existence and Large Time Behavior of Weak Solutions to Quantum Navier-Stokes-Poisson Equa-tions --- p.46 / Chapter 4.1 --- Global existence of weak solutions --- p.47 / Chapter 4.2 --- Large time behavior --- p.50 / Chapter 5 --- Discussions and Future Work --- p.55 / Bibliography --- p.56

This thesis examines the flow of very viscous Newtonian fluids driven by gravity. It is written with concern for specific applications in the optics industry, with emphasis on the slumping of molten glass into a mould, as in the manufacture of optical components, which are in turn used to manufacture ophthalmic lenses. This process is known as thermal replication. However, the work has more general applicability, and disc viscometry, used to determine the viscosity of very viscous fluids, is also considered. In addition, one chapter of the thesis is devoted to the flow of dripping honey, as another example of a very viscous flow to which the model can be applied. The Stokes creeping-flow equations are used to model the very viscous flows of interest. The main solution method is finite elements, and a purpose-written computer program has been developed to solve the creeping-flow equations by this method. The present program is restricted to solving for either two-dimensional or axisymmetric flows but is extendible to three dimensions. In addition, semi-analytic series and asymptotic methods are used for some small portions of the work. The optical applications of this work demand consideration of the topic of computing surface curvature, and therefore second derivatives, from inexact and discrete numerical and experimental data. For this purpose, fitting of B-splines by a least-squares method to coordinate data defining the surface has been used. Much of the work assumes isothermal conditions, but in the context of the accuracy required in optical component manufacture it is also possible that non-isothermal effects will be important. Consequently, this restriction is eventually relaxed and some consideration given to non-isothermal conditions. In order to validate the creeping-flow model and finite-element program, comparisons of numerical simulations with experimental results are performed. A preliminary assessment of the importance of non-isothermal conditions to the thermal-replication process is also made by comparing isothermal and non-isothermal simulations with experimental results. The isothermal model is found to best match the experimental data. / Thesis (Ph.D.)--School of Applied Mathematics, 1998.

No description available.

This thesis examines the flow of very viscous Newtonian fluids driven by gravity. It is written with concern for specific applications in the optics industry, with emphasis on the slumping of molten glass into a mould, as in the manufacture of optical components, which are in turn used to manufacture ophthalmic lenses. This process is known as thermal replication. However, the work has more general applicability, and disc viscometry, used to determine the viscosity of very viscous fluids, is also considered. In addition, one chapter of the thesis is devoted to the flow of dripping honey, as another example of a very viscous flow to which the model can be applied. The Stokes creeping-flow equations are used to model the very viscous flows of interest. The main solution method is finite elements, and a purpose-written computer program has been developed to solve the creeping-flow equations by this method. The present program is restricted to solving for either two-dimensional or axisymmetric flows but is extendible to three dimensions. In addition, semi-analytic series and asymptotic methods are used for some small portions of the work. The optical applications of this work demand consideration of the topic of computing surface curvature, and therefore second derivatives, from inexact and discrete numerical and experimental data. For this purpose, fitting of B-splines by a least-squares method to coordinate data defining the surface has been used. Much of the work assumes isothermal conditions, but in the context of the accuracy required in optical component manufacture it is also possible that non-isothermal effects will be important. Consequently, this restriction is eventually relaxed and some consideration given to non-isothermal conditions. In order to validate the creeping-flow model and finite-element program, comparisons of numerical simulations with experimental results are performed. A preliminary assessment of the importance of non-isothermal conditions to the thermal-replication process is also made by comparing isothermal and non-isothermal simulations with experimental results. The isothermal model is found to best match the experimental data. / Thesis (Ph.D.)--School of Applied Mathematics, 1998.

In this dissertation, I introduce a vortex method that is generally applicable to any two-dimensional, incompressible flow with or without boundaries. This method is deterministic, accurate, convergent, naturally adaptive, geometry independent and fully localized. For viscous flows, the vorticity distribution of each vortex element must evolve in addition to following a Lagrangian trajectory. My method relies upon an idea called core spreading. Core spreading is inconsistent by itself, but I have corrected it with a deterministic process known as "vortex fission" where one "fat" vortex is replaced by several "thinner" ones. Also, I examine rigorously a method for merging many blobs into one. This process maintains smaller problem sizes thus boosting the efficiency of the vortex method. To prove that this corrected core spreading method will converge uniformly, I adapted a continuous formalism to this grid-free scheme. This convergence theory does not rely on any form of grid. I only examine the linear problem where the flow field is specified, and treat the full nonlinear problem as a perturbation of the linear problem. The estimated rate of convergence is demonstrated to be sharp in several examples. Boundary conditions are approximated indirectly. The boundary is decomposed into a collection of small linear segments. I solve the no-slip and no-normal flow conditions simultaneously by superimposing a potential flow and injecting vorticity from the boundary consistent with the unsteady Rayleigh problem. Finally, the ultimate test for this new method is to simulate the wall jet. The simulations produce a dipole instability along the wall as observed in water tank and wind tunnel experiments and predicted by linear stability analysis. Moreover, the wavelength and height of these simulations agree quantitatively with experimental observations.

Finally, we prove that weak solutions to the compressible Navier-Stokes equations with the Navier boundary condition stabilize to static equilibrium states under a fair condition. / First, we show that the most general class of weak solutions to one-dimensional full compressible Navier-Stokes equations do not exhibit vacuum states in a finite time provided that no vacuum is present initially with the minimum physical assumptions on the data. Moreover, two initially non interacting vacuum regions will never meet each other in the future. / Secondly, we construct the local classical solutions to the compressible Navier-Stokes equations for initial vacuum far fields. In this case, we describe the blow-up phenomena of two-dimensional compact support smooth spherically symmetric solutions. When the far field of the initial state is away from vacuum, we obtain the global classical solutions and show the large time blow-up behavior of the gradient of the density. / This thesis deals with some important problems of compressible Navier-Stokes equations, including the well-posedness of the Cauchy problem, the regularity of the weak solutions constructed by Lions and Feireisl, and the dynamics of vacuum states, etc.. / Luo, Zhen. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 152-161). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

The two-dimensional, viscous flow around an elliptic cylinder undergoing prescribed unsteady motions is analyzed. The fluid is taken to be incompressible. Departing from the conventional vorticity-stream function approach, the Biot-Savart law of induced velocities is utilized to account for the contribution to the velocity field of the different vorticity fields comprising the flow. These include the internal vorticity due to the rotation of the body, the free vorticity in the fluid surrounding the body, and the bound vorticity distributed along the body contour. In order to apply the method, the body must be assumed to be replaced by fluid of the same density as the undisturbed surroundings. The replacement fluid must have a rigid motion exactly the same as the actual body motion. This can be achieved by placing suitable distributed vorticity fields within and on the surface of the body. The bound vorticity on the body surface is in the form of a vortex sheet, and its distribution is governed by a Fredholm integral equation of the second kind. The equation is derived in detail. It is solved numerically. The motion of the free vorticity in the flow field is governed by the Navier-Stokes equations written in terms of vorticity. The descretized vorticity transport equation is derived for a control volume and is solved numerically using an explicit method with a forward-difference for the time derivative, and a central-difference for the diffusive terms. An upwind method is used for convection terms. The results obtained using the present method are compared with a number of special cases available in the literature. Viscous flows around a circular cylinder rotating in any arbitrary fashion possess an exact solution, as presented in Chapter 2. Two cases of this flow are chosen for comparison. In the first case the circular cylinder is initially given an impulsive twist such that it rotates with a constant velocity about its axis. In the second case, the angular velocity of the circular cylinder increases with time exponentially. For a Reynolds number of 100, based on the cylinder radius and the internal vorticity, the exact solutions are compared with the numerical results. Viscous flow around an elliptic cylinder of .0996 aspect ratio rotating with a constant angular velocity is another special case, available in the literature, which is chosen for comparison. For this case the Reynolds number, based on the cylinder semi-major-axis and internal vorticity is 202. The agreement in all above-mentioned cases is excellent. Finally, viscous flow around an elliptic cylinder of .25 aspect ratio undergoing a combined translation and pitching oscillation is presented. A Reynolds number of 500, based on the semi-major-axis and body translational velocity, is chosen for this case. No similar case has been reported until now. This case, however, is only one of the many cases that can be handled by the present method.