Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds
By Dario Bambusi, Jean-Marc Delort, Benoît Grébert, Jérémie Szeftel. 2005
165 citations recorded by the source corpus.
This paper is devoted to the proof of almost global existence results for Klein‐Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc.
Subfields: Mathematical Physics, Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b772ad6dc3ee06503a691b9bce134a057f60679c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
- Michela Procesi
- Massimiliano Berti
- Livia Corsi
- Felice Iandoli
- Changxing Miao
- Dario Bambusi
- R. Feola
- P. Bolle
In Numerical Analysis
- Massimiliano Berti
- Michela Procesi
- Livia Corsi
- R. Feola
- Felice Iandoli
- Dario Bambusi
- P. Bolle
- Benoît Grébert
In Statistical and Nonlinear Physics
- Massimiliano Berti
- Michela Procesi
- Livia Corsi
- R. Feola
- Felice Iandoli
- Changxing Miao
- Dario Bambusi
- P. Bolle
Citations in the corpus
- A Birkhoff normal form theorem for some semilinear PDEs (2008, methodology): “The theory presented here was developed in [Bam03, BG06, DS06, BDGS07 , Gre06].”
- An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds (2013, methodology): “Interestingly, properties of this type have been used by Bambusi, Delort, Grébert, Szeftel [1] for Birkhoff normal form results of Klein-Gordon equations on Zoll manifolds (a main difficulty in [1] is to verify the Birkhoff normal form non-resonance conditions).”
- Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces (2011, methodology): “These properties have been recently used by Bambusi, Delort, Grebert, Szeftel [ 1 ], [17] to prove Birkho normal form stability results for wave equations.”
- Long time existence for fully nonlinear NLS with small Cauchy data on the circle (2018, background): “The paper [5] regards long time existence of solutions for the semi-linear Klein-Gordon equation on Zoll manifolds, here are collected all the ideas of the preceding (and aforementioned) literature.”
- Global well-posedness for Schrödinger equation with derivative in H 1 2 ( R ) (2009, methodology): “viously used in [23, 24]. However, it is of great complexity here and a dedicated multiplier analysis is needed in this situation. The resonant decomposition technical was also appeared previously in [2, 8, 13]. In particular, I-team [13] made use of the second generation “I-method”, a resonant deco”