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arXiv · 1712.05923

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

José A. Carrillo·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.

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José A. Carrillo, Young-Pil Choi, Oliver Tse. 2017-12-16. Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces. https://doi.org/10.1007/s00220-018-3276-8

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