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arXiv · 2208.00413

Almost global existence for some Hamiltonian PDEs with small Cauchy data on general tori

Dario Bambusi·Roberto Feola·Riccardo Montalto
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Abstract

In this paper we prove a result of almost global existence for some abstract nonlinear PDEs on flat tori and apply it to some concrete equations, namely a nonlinear Schr\"odinger equation with a convolution potential, a beam equation and a quantum hydrodinamical equation. We also apply it to the stability of plane waves in NLS. The main point is that the abstract result is based on a nonresonance condition much weaker than the usual ones, which rely on the celebrated Bourgain's Lemma which provides a partition of the "resonant sites" of the Laplace operator on irrational tori.

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Dario Bambusi, Roberto Feola, Riccardo Montalto. 2022-07-31. Almost global existence for some Hamiltonian PDEs with small Cauchy data on general tori. https://arxiv.org/abs/2208.00413

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