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University of Illinois at Urbana-Champaign
The Initial Value Problem for the Zakharov System
Abstract
dc:descriptionThe method of proof is an application of techniques developed by Bourgain and Kenig, Ponce and Vega. The equivalent fixed point problem is solved via the contraction principle in the $X\sb{s,b}$ spaces introduced by Bourgain. A detailed analysis of the nonlinear terms, exploiting the arithmetical properties of the $X\sb{s,b}$ denominators combined with the Strichartz estimates for the paraboloid, gives the d = 1, 2 results. For the more difficult d = 3 problem, Strichartz estimate for the cone and a refined convolution estimate for measures supported on the sphere are exploited to give the local result.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Colliander, James Ellis
- Contributors dc:contributor
-
- Jean Bourgain
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI9812563
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86949