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CERTAIN REGULARITY PROBLEMS IN FLUID DYNAMICS
by
Yuan Pei
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
Aug 2014
Copyright 2014 Yuan Pei
Object Description
| Title | Certain regularity problems in fluid dynamics |
| Author | Pei, Yuan |
| Author email | peimathatpku@gmail.com;ypei@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2014-04-30 |
| Date submitted | 2014-07-07 |
| Date approved | 2014-07-07 |
| Restricted until | 2014-07-07 |
| Date published | 2014-07-07 |
| Advisor (committee chair) | Kukavica, Igor |
| Advisor (committee member) |
Ziane, Mohammed Newton, Paul K. |
| Abstract | In the first chapter of this dissertation, we address the partial regularity for a suitable weak solutions of the Navier-Stokes system in a bounded space‐time domain D. We show that the parabolic fractal dimension of the singular set is less than or equal to 45/29, which is an improvement of the earlier result from [K4]. Also, we introduce the new λ-fractal dimension and prove that the dimension of the singular set is bounded by 3/2 for a certain range of λ. The second chapter addresses the existence and uniqueness of the solutions for the primitive equations of the ocean with continuous initial datum. We split the initial data into a regular finite energy part and a small bounded part and show that the equations are preserved by the splitting, which enables us to prove the well‐posedness of solutions. We provide a priori estimates and the construction of the solutions. |
| Keyword | Navier-Stokes equations; weak solutions; fractal dimension; regularity; primitive equations |
| Language | English |
| Format (imt) | application/pdf |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Contributing entity | University of Southern California |
| Rights | Pei, Yuan |
| Physical access | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-PeiYuan-2628.pdf |
| Archival file | uscthesesreloadpub_Volume14/etd-PeiYuan-2628.pdf |
Description
| Title | Page 1 |
| Repository email | cisadmin@lib.usc.edu |
| Full text | CERTAIN REGULARITY PROBLEMS IN FLUID DYNAMICS by Yuan Pei A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) Aug 2014 Copyright 2014 Yuan Pei |
