Existence of a Unique Solution to a System of Equations Modeling Compressible Fluid Flow with Capillary Stress Effects
<p> 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. T...
| Main Author: | |
|---|---|
| Language: | EN |
| Published: |
Texas A&M University - Corpus Christi
2018
|
| Subjects: | |
| Online Access: | http://pqdtopen.proquest.com/#viewpdf?dispub=10790012 |
| Summary: | <p> 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.</p><p> |
|---|