Workshops1-D Quintic NLS with White Noise Dispersion
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We consider the Cauchy problem for the 1-D quintic NLS with white noise dispersion. This equation is thought of as the limit of the NLS with random dispersion, which describes the propagation of a signal in an optical fiber with managed dispersion. We show the almost surely global existence of solution, no matter whether the coefficient of nonlinear term is positive or negative, while there are blowup solutions in the deternimistic focusing case. Our proof is based on the stochastic version of the Strichartz estimate. This is a joint work with Arnaud Debussche (Ecole Normale Superieure de Cachan, Attenne de Bretagne).
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Yoshio Tsutsumi
2011-01-14
09:00:00 - 09:50:00
R102 , Astronomy and Mathematics Building
We consider the Cauchy problem for the 1-D quintic NLS with white noise dispersion. This equation is thought of as the limit of the NLS with random dispersion, which describes the propagation of a signal in an optical fiber with managed dispersion. We show the almost surely global existence of solution, no matter whether the coefficient of nonlinear term is positive or negative, while there are blowup solutions in the deternimistic focusing case. Our proof is based on the stochastic version of the Strichartz estimate. This is a joint work with Arnaud Debussche (Ecole Normale Superieure de Cachan, Attenne de Bretagne).
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