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

We present an immersed interface algorithm for the incompressible Navier Stokes equations. The interface is represented by cubic splines which are interpolated through a set of Lagrangian control points. The position of the control points is implicitly updated using the fluid velocity. The forces that the interface exerts on the fluid are computed from the constitutive relation of the interface and are applied to the fluid through jumps in the pressure and jumps in the derivatives of pressure and velocity. A projection method is used to time advance the Navier-Stokes equations on a uniform cartesian mesh. The Poisson-like equations required for the implicit solution of the diffusive and pressure terms are solved using a fast Fourier transform algorithm. The position of the interface is updated implicitly using a quasi-Newton method (BFGS) within each timestep. Several examples are presented to illustrate the flexibility of the presented approach. / Singapore-MIT Alliance (SMA)

A new construction of regular solutions to the three dimensional Navier{Stokes equa- tions is introduced and applied to the study of their asymptotic expansions. This construction and other Phragmen-Linderl??of type estimates are used to establish su??- cient conditions for the convergence of those expansions. The construction also de??nes a system of inhomogeneous di??erential equations, called the extended Navier{Stokes equations, which turns out to have global solutions in suitably constructed normed spaces. Moreover, in these spaces, the normal form of the Navier{Stokes equations associated with the terms of the asymptotic expansions is a well-behaved in??nite system of di??erential equations. An application of those asymptotic expansions of regular solutions is the analysis of the helicity for large times. The dichotomy of the helicity's asymptotic behavior is then established. Furthermore, the relations between the helicity and the energy in several cases are described.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 73-77).

Thesis (M.S. in Aeronautical Engineering)--Naval Postgraduate School, September 2003. / Thesis advisor(s): Kevin D. Jones, Max F. Platzer. Includes bibliographical references (p. 55-56). Also available online.

Thesis--University of Kentucky (M.S.), 2003. / Title from document title page. Document formatted into pages; contains ix, 110 p. : ill. Includes abstract and vita. Includes bibliographical references (p. 99-109).

Thesis (Aeronautical and Astronautical Engineer)--Naval Postgraduate School, December 2002. / Thesis advisor(s): Kevin James, Max Platzer. Includes bibliographical references (p. 139). Also available online.

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