# Ill-posedness of the cubic nonlinear half-wave equation and other fractional NLS on the real line

Antoine Choffrut, Oana Pocovnicu

Research output: Contribution to journalArticlepeer-review

## Abstract

In this paper, we study ill-posedness of cubic fractional nonlinear Schr\"odinger equations. First, we consider the cubic nonlinear half-wave equation (NHW) on $\mathbb R$. In particular, we prove the following ill-posedness results: (i) failure of local uniform continuity of the solution map in $H^s(\mathbb R)$ for $s\in (0,\frac 12)$, and also for $s=0$ in the focusing case; (ii) failure of $C^3$-smoothness of the solution map in $L^2(\mathbb R)$; (iii) norm inflation and, in particular, failure of continuity of the solution map in $H^s(\mathbb R)$, $s 2$.
Original language English rnw246 41 International Mathematics Research Notices 2016 https://doi.org/10.1093/imrn/rnw246 Published - 24 Dec 2016

• math.AP

## Fingerprint

Dive into the research topics of 'Ill-posedness of the cubic nonlinear half-wave equation and other fractional NLS on the real line'. Together they form a unique fingerprint.