Pressureless Euler with nonlocal interactions as a singular limit of degenerate Navier-Stokes system

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:492

Article

Carrillo, Jose A.¹  Wroblewska-Kaminska, Aneta²  Zatorska, Ewelina³ 

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

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

[3] UCL, Dept Math, Gower St, London WC1E 6BT, England

关键词: Compressible Navier-Stokes equations;    Pressureless Euler equations;    Nonlocal attraction-repulsion;    Relative entropy;   

DOI  :  10.1016/j.jmaa.2020.124400

来源: Elsevier

【 摘 要 】

We show that weak solutions of degenerate Navier-Stokes equations converge to the strong solutions of the pressureless Euler system with linear drag term, Newtonian repulsion and quadratic confinement. The proof is based on the relative entropy method using the artificial velocity formulation for the one-dimensional Navier-Stokes system. (C) 2020 Published by Elsevier Inc.

【 授权许可】

Free