2000 character limit reached
Non-existence of solutions for the periodic cubic NLS below $L^2$
Published 21 Oct 2015 in math.AP | (1510.06208v2)
Abstract: We prove non-existence of solutions for the cubic nonlinear Schr\"odinger equation (NLS) on the circle if initial data belong to $Hs(\mathbb{T}) \setminus L2(\mathbb{T})$ for some $s \in (-\frac18, 0)$. 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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.