TY - JOUR

T1 - From gas dynamics with large friction to gradient flows describing diffusion theories

AU - Lattanzio, Corrado

AU - Tzavaras, Athanasios

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: AET was supported by funding from King Abdullah University of Science and
Technology (KAUST).

PY - 2016/12/12

Y1 - 2016/12/12

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/603947

UR - http://arxiv.org/abs/1601.05966

UR - http://www.scopus.com/inward/record.url?scp=85012913328&partnerID=8YFLogxK

U2 - 10.1080/03605302.2016.1269808

DO - 10.1080/03605302.2016.1269808

M3 - Article

VL - 42

SP - 261

EP - 290

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 2

ER -