Dissertation/Thesis Abstract

Existence of a Unique Solution to a System of Equations Modeling Compressible Fluid Flow with Capillary Stress Effects
by Cosper, Lane, M.Sc., Texas A&M University - Corpus Christi, 2018, 47; 10790012
Abstract (Summary)

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.

Indexing (document details)
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
Subjects: Fluid mechanics, Applied Mathematics, Mathematics
Keywords: Barotropic, Capillary, Compressible, Existence, Fluid, Navier
Publication Number: 10790012
ISBN: 978-0-438-00067-4
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