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|
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