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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.
Advisor: | Denny, Diane |
Commitee: | Palaniappan, Devanayagam, Sadovski, Alexey |
School: | Texas A&M University - Corpus Christi |
Department: | Mathematics |
School Location: | United States -- Texas |
Source: | MAI 57/06M(E), Masters Abstracts International |
Source Type: | DISSERTATION |
Subjects: | Fluid mechanics, Applied Mathematics, Mathematics |
Keywords: | Barotropic, Capillary, Compressible, Existence, Fluid, Navier |
Publication Number: | 10790012 |
ISBN: | 978-0-438-00067-4 |