Norm-inflation with Infinite Loss of Regularity 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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• Bulletin de la Société mathématique de France - View