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 language||English (US)|
|Number of pages||30|
|Journal||Communications in Partial Differential Equations|
|State||Published - Dec 12 2016|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: AET was supported by funding from King Abdullah University of Science and