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|Title: ||Some mathematical theories on the gas motion under the influence of external forcing|
|Other Titles: ||Yi xie guan yu wai li ying xiang xia qi ti yun dong de shu xue li lun|
|Authors: ||Duan, Renjun (段仁軍)|
|Department: ||Department of Mathematics|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2008|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Kinetic theory of gases.|
Fluid dynamics -- Mathematical models.
|Notes: ||CityU Call Number: QC175 .D83 2008|
vi, 261 leaves 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2008.
Includes bibliographical references (leaves -258)
|Abstract: ||This thesis is concerned with the mathematical study of the gas motion under the influence
of external forcing. The models considered are the Boltzmann equation in the
kinetic theory and the compressible Navier-Stokes equations in the fluid dynamics,
which have a close relation in the sense that the latter can be derived as an approximation
of second order from the former through the Chapman-Enskog expansion.
In the first part, the Cauchy problems on the Boltzmann equation near vacuum or
Maxwellians are investigated for the case when the external forces are present. Global
existence and uniform in time stability of solutions are proved in the framework of
small perturbations. Moreover, the optimal rate of convergence of the solution to the
Maxwellian is obtained by combining the refined high-order energy estimates with the
spectral analysis. The same method is applied to the general time-dependent external
force, especially the time-periodic one for which the existence and asymptotical stability
of the time-periodic solution with the same period is proved if the spatial dimension
is not less than five.
In the second part, two mathematical results about the compressible Navier-Stokes
equations with external forces are obtained. One is the global existence and uniqueness
of weak solutions to the initial boundary value problem for the one dimensional
isentropic Navier-Stokes equations under the gravitational force when the viscosity
depends on the density and the initial density is continuously connected to vacuum.
The other one, whose proof is similar as in the case of the Boltzmann equation, is
the optimal Lp-Lq convergence rate of solutions to the Cauchy problem for the threedimensional
Navier-Stokes equations with a potential force.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b2340671|
|Appears in Collections:||MA - Doctor of Philosophy |
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