Poincaré-Dulac normal form reduction for unconditional well-posedness of the periodic cubic NLS

Zihua Guo, Soonsik Kwon, Tadahiro Oh

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)19-48
Number of pages30
JournalCommunications in Mathematical Physics
Volume322
Issue number1
DOIs
Publication statusPublished - 2013

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