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

Zihua Guo, Soonsik Kwon, Tadahiro Oh

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20 Citations (Scopus)

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 CtL2(T), without using any auxiliary function space. This allows us to construct weak solutions of NLS in CtL2(T) with initial data in L2(T) as limits of classical solutions. As a consequence of our construction, we also prove unconditional well-posedness of NLS in Hs(T) for Hs? 1/6.
Original languageEnglish
Pages (from-to)19 - 48
Number of pages30
JournalCommunications in Mathematical Physics
Volume322
Issue number1
DOIs
Publication statusPublished - 2013
Externally publishedYes

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