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|Title: ||Some problems on Navier-Stokes equations and Boltzmann equations|
|Other Titles: ||Guan yu Navier-Stokes fang cheng he Boltzmann fang cheng de mou xie wen ti|
關於 Navier-Stokes 方程和 Boltzmann 方程的某些問題
|Authors: ||Ma, Hongfang (馬紅芳)|
|Department: ||Department of Mathematics|
|Degree: ||Master of Philosophy|
|Issue Date: ||2007|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Fluid dynamics.|
|Notes: ||51 leaves 30 cm.|
Thesis (M.Phil.)--City University of Hong Kong, 2007.
Includes bibliographical references (leaves -51)
CityU Call Number: QA911 .M33 2007
|Abstract: ||In this thesis, we study some problems on the Navier-Stokes equations and Boltzmann-
Enskog equation which are in the active research area of applied mathematics.
The system of Navier-Stokes equations is a typical example of the conservation
laws. In the first part of the thesis, we study the global existence and convergence rates
of solutions to the three-dimensional compressible Navier-Stokes equations without
heat conductivity. The velocity is dissipative because of the viscosity, whereas the entropy
is non-dissipative due to the absence of heat conductivity. The global solution
is obtained by combining the local existence and a priori estimates if H3-norm of the
initial perturbation around a constant state is small enough and its L1-norm is bounded.
A priori decay-in-time estimates on the pressure and velocity are used to get the uniform
bound of entropy. Moreover, the optimal convergence rates are also obtained.
The result has accepted for publication in Indiana University Mathematics Journal.
On the other hand, the Boltzmann equation coming from the statistic physics is
a fundamental equation in the kinetic theory for the rarefied gas. In the second part
of this thesis, we study the half-space problem of the nonlinear Boltzmann-Enskog
equation, assigning the Dirichlet data for the incoming particles at the boundary and
a Maxwellian at the far field. It is an ongoing research project. The main part of
the proof has been completed except Lemma 2.5. We want to show that if the far
field Mach numberM1 < −1, there exists a unique smooth solution connecting the
Dirichlet data and the far Maxwellian for any Dirichlet data sufficiently close to the
far field Maxwellian. As a byproduct, the same holds for the linearized problem. The
proof is essentially based on the macro-micro or hydrodynamics-kinetic decomposition
of solutions and the energy estimate.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b2268767|
|Appears in Collections:||MA - Master of Philosophy |
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