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Article Dans Une Revue Mathematical Research Letters Année : 2009

On ill-posedness for the one-dimensional periodic cubic Schrodinger equation

Résumé

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\neq 0 $. This result is slightly stronger than the one obtained by Christ-Colliander-Tao 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 $ L^2(\T) $.
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Dates et versions

hal-00291648 , version 1 (27-06-2008)
hal-00291648 , version 2 (02-07-2008)

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Citer

Luc Molinet. On ill-posedness for the one-dimensional periodic cubic Schrodinger equation. Mathematical Research Letters, 2009, 16 (1), pp.111-120. ⟨hal-00291648v2⟩
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