Relative entropy method for the relaxation limit of hydrodynamic models

作者：José A. Carrillo, Yingping Peng, Aneta Wróblewska‐Kamińska · 发表于：Networks and Heterogeneous Media · 年份：2020 · DOI：10.3934/nhm.2020023 · 被引用次数：19 · 研究领域：Navier-Stokes equation solutions、Mathematical Biology Tumor Growth、Advanced Mathematical Physics Problems

We show how to obtain general nonlinear aggregation-diffusion models, including Keller-Segel type models with nonlinear diffusions, as relaxations from nonlocal compressible Euler-type hydrodynamic systems via the relative entropy method. We discuss the assumptions on the confinement and interaction potentials depending on the relative energy of the free energy functional allowing for this relaxation limit to hold. We deal with weak solutions for the nonlocal compressible Euler-type systems and strong solutions for the limiting aggregation-diffusion equations. Finally, we show the existence of weak solutions to the nonlocal compressible Euler-type systems satisfying the needed properties for completeness sake.