Work

Almost global existence for some Hamiltonian PDEs on manifolds with globally integrable geodesic flow

Year: 2025

Type: article

Abstract: In this paper we prove an abstract result of almost global existence for small and smooth solutions of some semilinear PDEs on Riemannian manifolds with globally integrable geodesic flow. Some examples of such manifolds are Lie groups (including flat tori), homogeneous spaces and rotational invariant surfaces. As applications of the abstract result we prove almost global existence for a nonlinear Schrödinger equation with a convolution potential and for a nonlinear beam equation. We also prove Hs stability of the ground state in NLS equation. The proof is based on a normal form procedure and the combination of the arguments used in Bambusi and Langella (2022 arXiv:2202.04505) to bound the growth of Sobolev norms in linear systems and a generalization of the arguments in Bambusi et al (2024 Commun. Math. Phys. 405 253–85).

Source: Nonlinearity

DOI: 10.1088/1361-6544/adc967

Authors: D Bambusi, R Feola, B Langella, F Monzani

Institutions: University of Milan, Roma Tre University, Scuola Internazionale Superiore di Studi Avanzati

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca, Gruppo Nazionale per la Fisica Matematica, Ministero dell'Istruzione e del Merito