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
SN - 0360-5302
VL - 42
SP - 261
EP - 290
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 2
ER -