Work

Large time nonlinear dynamics close to inhomogeneous stationary states of the Vlasov-HMF model

Year: 2026

Type: preprint

Abstract: We consider the Vlasov-HMF (Hamiltonian Mean-Field) model and symmetric perturbations of symmetric inhomogeneous stationary states that are naturally associated with a pendulum Hamiltonian flow. We first show the existence of families of such stationary states having compact support inside the separatrix region, constant value near the origin, and satisfying a linear stability (Penrose) criterion. We then describe the nonlinear dynamics of small compactly supported perturbations with finite regularity of this class of equilibria. More precisely, we prove that for large (but finite) times, in a modulated action-angle coordinate system the solution remains close to a modulated stationary state and that the magnetization of the perturbation satisfes decay estimates driven by the linear dynamics.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.16998

Authors: Faou, Erwan, Rousset, Frédéric, Seetohul, Tooryanand

Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Centre Inria de l'Université de Rennes, École Normale Supérieure de Rennes, Institut de recherche mathématique de Rennes, Université de Rennes

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation, Boundaries, Congestion and Vorticity in Fluids: A connection with environmental issues, KAM Theory, PDE and Numerics, G7080048889

OpenAlex ID: W7213392734

Cites: 7

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Related to: 10