Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces
arXiv:1712.05923 · doi:10.1007/s00220-018-3276-8
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.