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

Zihua Guo; Tadahiro Oh

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

Analysis of PDEs 2016-11-29 v2

Authors: Zihua Guo , Tadahiro Oh

Abstract

We prove non-existence of solutions for the cubic nonlinear Schr\"odinger equation (NLS) on the circle if initial data belong to $H^s(\mathbb{T}) \setminus L^2(\mathbb{T})$ 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.

Keywords

cubic nonlinear Schrödinger equation periodic domain non-existence of solutions negative Sobolev spaces Fourier restriction norm method a priori bound

Cite

@article{arxiv.1510.06208,
  title  = {Non-existence of solutions for the periodic cubic NLS below $L^2$},
  author = {Zihua Guo and Tadahiro Oh},
  journal= {arXiv preprint arXiv:1510.06208},
  year   = {2016}
}

Comments

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

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