RELATIVE ENTROPY METHOD FOR THE RELAXATION LIMIT OF HYDRODYNAMIC MODELS

被引：17

作者：

Carrillo, Jose Antonio ^{[1
]}

Peng, Yingping ^{[2
,3
]}

Wroblewska-Kaminska, Aneta ^{[4
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

[2] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Peoples R China

[3] Imperial Coll London, Dept Math, London SW7 2AZ, England

[4] Polish Acad Sci, Inst Math, Sniadeckich 8, PL-00656 Warsaw, Poland

来源：

NETWORKS AND HETEROGENEOUS MEDIA | 2020年 / 15卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Relative entropy method; aggregation-diffusions; nonlocal hydrodynamics; relaxation limit; COMPRESSIBLE EULER EQUATIONS; WEAK SOLUTIONS; LARGE FRICTION; CONVERGENCE; SYSTEM; DIFFUSION; STABILITY; EXISTENCE; SPACE; MASS;

D O I：

10.3934/nhm.2020023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：369 / 387

页数：19

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