Norm-inflation for periodic NLS equations in negative Sobolev spaces

Abstract

In this paper we consider Schr{ö}dinger equations with nonlinearities of odd order 2$\sigma$ + 1 on T^d. We prove that for $\sigma$d$\ge$2, they are strongly illposed in the Sobolev space H^s for any s \textless{} 0, exhibiting norm-inflation with infinite loss of regularity. In the case of the one-dimensional cubic nonlinear Schr{ö}dinger equation and its renormalized version we prove such a result for H^s with s \textless{} --2/3.

18 pages

References in corpus (1)

• Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data

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