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

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

2011-03-28

arxiv.org/abs/1103.5271v3

Mathematics

Analysis of PDEs

28 pages. In Section 3, we now use (ordered) trees for indexing multilinear terms appearing in the process (instead of assumin

Scientific paper

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.

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