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Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential

TitleQuasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential
Publication TypeJournal Article
Year of Publication2013
AuthorsBerti, M, Bolle, P
JournalJournal of the European Mathematical Society
Volume15
Pagination229-286
ISSN14359855
Abstract

We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on Td , d ≥ 1, finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are C∞ then the solutions are C∞. The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators ("Green functions") along scales of Sobolev spaces. The key off-diagonal decay estimates of the Green functions are proved via a new multiscale inductive analysis. The main novelty concerns the measure and "complexity" estimates. © European Mathematical Society 2013.

DOI10.4171/JEMS/361

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