TY - JOUR
T1 - Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential
JF - Journal of the European Mathematical Society
Y1 - 2013
A1 - Massimiliano Berti
A1 - Philippe Bolle
AB - 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.
VL - 15
N1 - cited By (since 1996)5
ER -