### 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 language | English |
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Pages (from-to) | 329-361 |

Number of pages | 33 |

Journal | Communications in Mathematical Physics |

Volume | 365 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2019 Jan 24 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Carrillo, J. A., Choi, Y. P., & Tse, O. (2019). Convergence to Equilibrium in Wasserstein Distance for Damped Euler Equations with Interaction Forces.

*Communications in Mathematical Physics*,*365*(1), 329-361. https://doi.org/10.1007/s00220-018-3276-8