Convergence to equilibrium in Wasserstein distance for damped Euler equations with interaction forces
File(s)
Published version
Author(s)
Carrillo de la Plata, J
Choi, Young-Pil
Tse, Oliver
Type
Journal Article
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.
Date Issued
2019-01-31
Date Acceptance
2018-08-29
Citation
Communications in Mathematical Physics, 2019, 365 (1), pp.329-361
ISSN
0010-3616
Publisher
Springer Verlag
Start Page
329
End Page
361
Journal / Book Title
Communications in Mathematical Physics
Volume
365
Issue
1
Copyright Statement
© 2018 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/P031587/1
Subjects
Science & Technology
Physical Sciences
Physics, Mathematical
Physics
NONLINEAR DIFFUSION WAVES
STRONG RELAXATION LIMIT
GLOBAL BV SOLUTIONS
ASYMPTOTIC-BEHAVIOR
CONSERVATION-LAWS
P-SYSTEM
PARTICLE
AGGREGATION
EXISTENCE
ENTROPY
0105 Mathematical Physics
0206 Quantum Physics
0101 Pure Mathematics
Mathematical Physics
Publication Status
Published
Date Publish Online
2018-10-04