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MSRI Summer Microprogram on Nonlinear Partial Differential Equations |
| July 23, 2007 to August 10, 2007 |
| Organized By: L. C. Evans (UC Berkeley, Chair), C. Gutierrez (Temple), C. Sogge (Johns Hopkins), D. Tataru (UC Berkeley) |
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| Return to Workshop Description |
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An a priori bound and weak solvability of the nonlinear Schrodinger equation
Monday August 6, 2007
09:00AM - 10:00AM
Speakers:
Michael Christ
Abstract:
An a priori bound holds for solutions of the cubic one-dimensional nonlinear Schrodinger equation in Sobolev spaces of certain negative orders, for sufficiently small finite time. Weak solutions to the Cauchy problem exist for arbitrary initial data in these spaces. The analysis relies on (trilinear) Strichartz estimates and certain variants of the X spaces of Bourgain.
This is joint work with J. Colliander and T. Tao. Such bounds were proved independently by H. Koch and D. Tataru.
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