Non-existence of solutions for the periodic cubic NLS below $L^2$

Abstract

We prove non-existence of solutions for the cubic nonlinear Schrödinger equation (NLS) on the circle if initial data belong to $H^s(\mathbb{T})\setminus L^2(\mathbb{T})$ for some $s\in (-\frac{1}{8},0)$. The proof is based on establishing an a priori bound on solutions to a renormalized cubic NLS in negative Sobolev spaces via the short time Fourier restriction norm method.

56 pages. To appear in Internat. Math. Res. Not

References in corpus (5)

• Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data
• Instability of the periodic nonlinear Schrodinger equation
• Norm-inflation for periodic NLS equations in negative Sobolev spaces
• On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle
• Rough solutions of the fifth-order KdV equations

Cited by in corpus (1)

• On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle