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ANALYTICITY AND GEVREY-CLASS REGULARITY FOR THE EULER
EQUATIONS
by
Vlad Cristian Vicol
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
August 2010
Copyright 2010 Vlad Cristian Vicol
Object Description
| Title | Analyticity and Gevrey-class regularity for the Euler equations |
| Author | Vicol, Vlad Cristian |
| Author email | vlad.vicol@gmail.com; vicol@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2010-05-24 |
| Date submitted | 2010 |
| Restricted until | Unrestricted |
| Date published | 2010-07-23 |
| Advisor (committee chair) | Kukavica, Igor |
| Advisor (committee member) |
Friedlander, Susan Lototsky, Sergey Newton, Paul Ziane, Mohammed |
| Abstract | The Euler equations are the classical model for the motion of an incompressible inviscid homogeneous fluid. This thesis addresses geometric qualitative properties of smooth solutions to the Euler equations, namely the persistence of analyticity and Gevrey-class regularity on domains with smooth boundary.; The structure of the spectrum of solutions to the three-dimensional Euler equations is a problem of fundamental interest in turbulence theory. The size of the uniform real-analyticity radius of the solution provides an estimate for the scale below which the Fourier coefficients decay exponentially; it moreover gives the rate of this exponential decay. This thesis also addresses the problem of finding sharp lower bounds for the uniform real-analyticity and Gevrey-class regularity radius of the solutions. We prove that the rate of decay of the radius depends at most exponentially on the supremum of the velocity gradient, and algebraically on the higher Sobolev norms of the solution. |
| Keyword | analyticity radius; Euler equations; Gevrey-class |
| Language | English |
| 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-m3214 |
| Rights | Vicol, Vlad Cristian |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Vicol-3909 |
| Archival file | uscthesesreloadpub_Volume35/etd-Vicol-3909.pdf |
Description
| Title | Page 1 |
| Full text | ANALYTICITY AND GEVREY-CLASS REGULARITY FOR THE EULER EQUATIONS by Vlad Cristian Vicol A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MATHEMATICS) August 2010 Copyright 2010 Vlad Cristian Vicol |
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