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Title:The Initial Value Problem for the Zakharov System
Author(s):Colliander, James Ellis
Doctoral Committee Chair(s):Jean Bourgain
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Physics, Fluid and Plasma
Abstract:The 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.
Issue Date:1997
Type:Text
Language:English
Description:74 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.
URI:http://hdl.handle.net/2142/86949
Other Identifier(s):(MiAaPQ)AAI9812563
Date Available in IDEALS:2015-09-28
Date Deposited:1997


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