A remark on norm inflation with general initial data for the cubic nonlinear Schrödinger equations in negative Sobolev spaces
arXiv:1509.08143
Abstract
In this note, we consider the ill-posedness issue for the cubic nonlinear Schrödinger equation. In particular, we prove norm inflation based at every initial condition in negative Sobolev spaces below or at the scaling critical regularity.
18 pages. Updated references
References in corpus (5)
- Ill-posedness for nonlinear Schrodinger and wave equations
- Instability of the periodic nonlinear Schrodinger equation
- Norm-inflation for periodic NLS equations in negative Sobolev spaces
- Generic ill-posedness for wave equation of power type on 3D torus
- On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle