Poincar\'e-Dulac normal form reduction for unconditional well-posedness of the periodic cubic NLS
Analysis of PDEs
2011-09-07 v3 Dynamical Systems
Abstract
We implement an infinite iteration scheme of Poincare-Dulac normal form reductions to establish an energy estimate on the one-dimensional cubic nonlinear Schrodinger equation (NLS) in C_t L^2(T), without using any auxiliary function space. This allows us to construct weak solutions of NLS in C_t L^2(T)$ with initial data in L^2(T) as limits of classical solutions. As a consequence of our construction, we also prove unconditional well-posedness of NLS in H^s(T) for s \geq 1/6.
Keywords
Cite
@article{arxiv.1103.5271,
title = {Poincar\'e-Dulac normal form reduction for unconditional well-posedness of the periodic cubic NLS},
author = {Zihua Guo and Soonsik Kwon and Tadahiro Oh},
journal= {arXiv preprint arXiv:1103.5271},
year = {2011}
}
Comments
28 pages. In Section 3, we now use (ordered) trees for indexing multilinear terms appearing in the process (instead of assuming that the time derivative falls on the first factor as in the previous version.)