Convergence to Equilibrium in Wasserstein Distance for Damped Euler Equations with Interaction Forces

José A. Carrillo; Young Pil Choi; Oliver Tse

doi:10.1007/s00220-018-3276-8

Convergence to Equilibrium in Wasserstein Distance for Damped Euler Equations with Interaction Forces

José A. Carrillo, Young Pil Choi, Oliver Tse

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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
Pages (from-to)	329-361
Number of pages	33
Journal	Communications in Mathematical Physics
Volume	365
Issue number	1
DOIs	https://doi.org/10.1007/s00220-018-3276-8
Publication status	Published - 2019 Jan 24

Bibliographical note

Funding Information:
JAC was partially supported by the EPSRC grant number EP/P031587/1. YPC was supported by National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (Nos. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. The authors are very grateful to the Mittag-Leffler Institute for providing a fruitful working environment during the special semester Interactions between Partial Differential Equations & Functional Inequalities.

Funding Information:
Acknowledgements JAC was partially supported by the EPSRC grant number EP/P031587/1. YPC was supported by National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (Nos. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. The authors are very grateful to the Mittag-Leffler Institute for providing a fruitful working environment during the special semester Interactions between Partial Differential Equations & Functional Inequalities.

Publisher Copyright:
© 2018, The Author(s).

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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Cite this

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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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note = "Funding Information: JAC was partially supported by the EPSRC grant number EP/P031587/1. YPC was supported by National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (Nos. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. The authors are very grateful to the Mittag-Leffler Institute for providing a fruitful working environment during the special semester Interactions between Partial Differential Equations & Functional Inequalities. Funding Information: Acknowledgements JAC was partially supported by the EPSRC grant number EP/P031587/1. YPC was supported by National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (Nos. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. The authors are very grateful to the Mittag-Leffler Institute for providing a fruitful working environment during the special semester Interactions between Partial Differential Equations & Functional Inequalities. Publisher Copyright: {\textcopyright} 2018, The Author(s).",

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Convergence to Equilibrium in Wasserstein Distance for Damped Euler Equations with Interaction Forces

Abstract

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