10-194 Massimiliano Berti, Philippe Bolle

Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential (797K, Pdf) Dec 3, 10

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Abstract. We prove the existence of quasi-periodic solutions for Schr"odinger equations with a multiplicative potential on Td, d >= 1, merely di fferentiable 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 C1 then the solutions are C1. 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 o -diagonal decay estimates of the Green functions are proved via a new multiscale inductive analysis. The main novelty concerns the measure and "complexity" estimates.

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