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.

Almost Global Existence for Some Hamiltonian PDEs with Small Cauchy Data on General Tori / D. Bambusi, R. Feola, R. Montalto. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 405:1(2024), pp. 15.1-15.50. [10.1007/s00220-023-04899-z]

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

D. Bambusi
Primo
;
R. Montalto
Ultimo
2024

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 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.
Settore MAT/07 - Fisica Matematica
Settore MAT/05 - Analisi Matematica
   Hamiltonian Dynamics, Normal forms and Water Waves (HamDyWWa)
   HamDyWWa
   EUROPEAN COMMISSION
   101039762

   Hamiltonian and dispersive PDE's
   MINISTERO DELL'ISTRUZIONE E DEL MERITO
   2020XB3EFL_005
2024
25-gen-2024
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1051168
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