Poincare-Dulac Normal Form Reduction for Unconditional Well-Posedness of the Periodic Cubic NLS

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We implement an infinite iteration scheme of Poincar,-Dulac normal form reductions to establish an energy estimate on the one-dimensional cubic nonlinear Schrodinger equation (NLS) in , without using any auxiliary function space. This allows us to construct weak solutions of NLS in with initial data in as limits of classical solutions. As a consequence of our construction, we also prove unconditional well-posedness of NLS in for s >= 1/6.
Publisher
SPRINGER
Issue Date
2013-08
Language
English
Article Type
Article
Keywords

NONLINEAR SCHRODINGER-EQUATION; ILL-POSEDNESS; KDV EQUATION; I-METHOD; H-S

Citation

COMMUNICATIONS IN MATHEMATICAL PHYSICS, v.322, no.1, pp.19 - 48

ISSN
0010-3616
DOI
10.1007/s00220-013-1755-5
URI
http://hdl.handle.net/10203/175546
Appears in Collection
MA-Journal Papers(저널논문)
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