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

Published 16 Dec 2017 in math.AP | (1712.05923v2)

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.

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