Almost Global Existence for Some Hamiltonian PDEs with Small Cauchy Data on General Tori

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 Schrödinger equation with a convolution potential, a beam equation and a quantum hydrodinamical equation. We also apply it to the stabi...

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Bibliographic Details
Published in:Communications in mathematical physics 2024, Vol.405 (1), p.15-15, Article 15
Main Authors: Bambusi, D., Feola, R., Montalto, R.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Nonresonance
Physics
Physics and Astronomy
Plane waves
Quantum Physics
Relativity Theory
Schrodinger equation
Theoretical
Toruses
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Summary: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 Schrödinger 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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-023-04899-z