We prove the existence of quasi-periodic solutions of Schrodinger equations on any d-dimensional torus, with nonlinearities which are merely differentiable functions. Our solutions have only Sobolev regularity both in time and space. The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators along scales of Sobolev spaces. We prove these linear estimates via a new multiscale inductive analysis.

Sobolev quasi-periodic solutions of NLS in any spatial dimension

BERTI, MASSIMILIANO
2010

Abstract

We prove the existence of quasi-periodic solutions of Schrodinger equations on any d-dimensional torus, with nonlinearities which are merely differentiable functions. Our solutions have only Sobolev regularity both in time and space. The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators along scales of Sobolev spaces. We prove these linear estimates via a new multiscale inductive analysis.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/364418
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