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Norm-inflation for periodic NLS equations in negative Sobolev spaces

Abstract : In this paper we consider Schrödinger equations with nonlinearities of odd order 2σ + 1 on T^d. We prove that for σd≥2, they are strongly illposed in the Sobolev space H^s for any s < 0, exhibiting norm-inflation with infinite loss of regularity. In the case of the one-dimensional cubic nonlinear Schrödinger equation and its renormalized version we prove such a result for H^s with s < −2/3.
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https://hal.archives-ouvertes.fr/hal-01176513
Contributor : Rémi Carles Connect in order to contact the contributor
Submitted on : Wednesday, July 15, 2015 - 3:07:11 PM
Last modification on : Wednesday, October 5, 2022 - 3:28:52 PM
Long-term archiving on: : Friday, October 16, 2015 - 11:06:07 AM

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Rémi Carles, Thomas Kappeler. Norm-inflation for periodic NLS equations in negative Sobolev spaces. Bulletin de la société mathématique de France, 2017, 145 (4), pp.623-642. ⟨10.24033/bsmf.2749⟩. ⟨hal-01176513⟩

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