Advances in the theory of dispersive equations

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Advances in the Theory of Dispersive Equations Abstract of Proposed ResearchGigliola Staffilani This project is to study the well posedness of dispersive partial differential equations, with particular emphasis on the nonlinear Schroedinger equation. That is, how much regularity must one impose on the initial data to insure existence and uniqueness of the solutions at later times? Also what regularity is preserved and what is the asymptotic behavior of the solutions? Recent advances in the theory of nonlinear dispersive equations have been driven by the introduction of sophisticated methods and new techniques from Fourier and harmonic analysis. This proposal is to further pursue these new directions and to better understand their implications.