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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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