Existence of a Unique Solution to a System of Equations Modeling Compressible Fluid Flow with Capillary Stress Effects

• Main Author: Cosper, Lane
• Language: EN
• Published: Texas A&M University - Corpus Christi 2018
• Subjects: Fluid mechanics|Applied mathematics|Mathematics
• Online Access: http://pqdtopen.proquest.com/#viewpdf?dispub=10790012

<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>