Existence of a unique solution to a system of equations modeling compressible fluid flow with capillary stress effects
| dc.contributor.advisor | Denny, Diane | |
| dc.contributor.author | Cosper, Lane | |
| dc.contributor.committeeMember | Palaniappan, Devanayagam | |
| dc.contributor.committeeMember | Sadovski, Alexey L. | |
| dc.date.accessioned | 2018-10-17T16:29:06Z | |
| dc.date.available | 2018-10-17T16:29:06Z | |
| dc.date.issued | 2018-05 | |
| dc.description.abstract | 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. | en_US |
| dc.description.college | College of Science and Engineering | en_US |
| dc.description.department | Mathematics and Statistics | en_US |
| dc.format.extent | 41 pages | en_US |
| dc.identifier.uri | https://tamucc-ir.tdl.org/handle/1969.6/87008 | |
| dc.language.iso | en_US | en_US |
| dc.rights | Attribution 3.0 United States | * |
| dc.rights | This material is made available for use in research, teaching, and private study, pursuant to U.S. Copyright law. The user assumes full responsibility for any use of the materials, including but not limited to, infringement of copyright and publication rights of reproduced materials. Any materials used should be fully credited with its source. All rights are reserved and retained regardless of current or future development or laws that may apply to fair use standards. Permission for publication of this material, in part or in full, must be secured with the author and/or publisher. | en_US |
| dc.rights.uri | http://creativecommons.org/licenses/by/3.0/us/ | * |
| dc.subject | barotropic | en_US |
| dc.subject | capillary | en_US |
| dc.subject | compressible | en_US |
| dc.subject | existence | en_US |
| dc.subject | fluid | en_US |
| dc.subject | Navier | en_US |
| dc.title | Existence of a unique solution to a system of equations modeling compressible fluid flow with capillary stress effects | en_US |
| dc.type | Text | en_US |
| dc.type.genre | Thesis | en_US |
| thesis.degree.discipline | Mathematics | en_US |
| thesis.degree.grantor | Texas A & M University--Corpus Christi | en_US |
| thesis.degree.level | Masters | en_US |
| thesis.degree.name | Master of Science | en_US |