From gas dynamics with large friction to gradient flows describing diffusion theories

Corrado Lattanzio, Athanasios Tzavaras

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow in the diffusive limit regime. We apply this approach to prove convergence from the Euler-Poisson system with friction to the Keller-Segel system in the regime that the latter has smooth solutions. The same methodology is used to establish convergence from the Euler-Korteweg theory with monotone pressure laws to the Cahn-Hilliard equation.
Original languageEnglish (US)
Pages (from-to)261-290
Number of pages30
JournalCommunications in Partial Differential Equations
Volume42
Issue number2
DOIs
StatePublished - Dec 12 2016

Fingerprint

Dive into the research topics of 'From gas dynamics with large friction to gradient flows describing diffusion theories'. Together they form a unique fingerprint.

Cite this