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ON ILL-POSEDNESS FOR THE ONE-DIMENSIONAL PERIODIC CUBIC SCHRODINGER EQUATION

By Luc Molinet

Abstract

We prove the ill-posedness in H s (T), s < 0, of the periodic cubic Schrödinger equation in the sense that the flow-map is not continuous from H s (T) into itself for any fixed t = 0. This result is slightly stronger than the one in [7] where the discontinuity of the solution map is established. Moreover our proof is different and clarifies the ill-posedness phenomena. Our approach relies on a new result on the behavior of the associated flow-map with respect to the weak topology of L²(T)

Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.311.6253
Provided by: CiteSeerX
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