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Journal Articles Archive for Rational Mechanics and Analysis Year : 2017

Nonlinear stability criteria for the HMF Model

Abstract

We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the Hamiltonian Mean Field (HMF) model. Under a specific criterion, we prove the nonlinear stability of steady states which are decreasing functions of the microscopic energy. To achieve this task, we extend to this context the strategy based on generalized rearrangement techniques which was developed recently for the gravitational Vlasov-Poisson equation. Explicit stability inequalities are established and our analysis is able to treat non compactly supported steady states to HMF, which are physically relevant in this context but induces additional difficulties, compared to the Vlasov-Poisson system.
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Dates and versions

hal-01207626 , version 1 (30-01-2017)

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Mohammed Lemou, Ana Maria Luz, Florian Méhats. Nonlinear stability criteria for the HMF Model. Archive for Rational Mechanics and Analysis, 2017, 224 (2), pp.353-380. ⟨10.1007/s00205-017-1077-4⟩. ⟨hal-01207626⟩
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