Convergence to equilibrium in Wasserstein distance for damped Euler equations with interaction forces

José A. Carrillo (Corresponding author), Young Pil Choi, Oliver Tse

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Abstract

We develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces with respect to the 2-Wasserstein distance. We also discuss the overdamped limit to a nonlocal equation used in the modelling of granular media with respect to the 2-Wasserstein distance, and provide rigorous proofs for particular examples in one spatial dimension.

Original languageEnglish
Pages (from-to)329-361
Number of pages33
JournalCommunications in Mathematical Physics
Volume365
Issue number1
Early online date4 Oct 2018
DOIs
Publication statusPublished - 24 Jan 2019

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