The purpose of this thesis is to prove the existence of a unique solution to a system of partial differential equations which models the flow of a compressible barotropic fluid under periodic boundary conditions. The equations come from modifying the compressible Navier-Stokes equations. The proof utilizes the method of successive approximations. We will define an iteration scheme based on solving a linearized version of the equations. Then convergence of the sequence of approximate solutions to a unique solution of the nonlinear system will be proven. The main new result of this thesis is that the density data is at a given point in the spatial domain over a time interval instead of an initial density over the entire spatial domain. Further applications of the mathematical model are fluid flow problems where the data such as concentration of a solute or temperature of the fluid is known at a given point. Future research could use boundary conditions which are not periodic.
|Commitee:||Palaniappan, Devanayagam, Sadovski, Alexey|
|School:||Texas A&M University - Corpus Christi|
|School Location:||United States -- Texas|
|Source:||MAI 57/06M(E), Masters Abstracts International|
|Subjects:||Fluid mechanics, Applied Mathematics, Mathematics|
|Keywords:||Barotropic, Capillary, Compressible, Existence, Fluid, Navier|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
supplemental files is subject to the ProQuest Terms and Conditions of use.