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

Author: 

Carrillo de la Plata, J
Choi, Y
Tse, O

Publication Date: 

4 October 2018

Journal: 

Communications in Mathematical Physics

Last Updated: 

2020-10-31T07:44:01.917+00:00

Issue: 

1

Volume: 

365

DOI: 

10.1007/s00220-018-3276-8

page: 

329-361

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.

Symplectic id: 

1098232

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article