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

2019/06/03 by Carrillo, José A., Wróblewska-Kamińska, Aneta, Zatorska, Ewelina · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.00664

Abstract

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.

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• Existence and weak-strong uniqueness of measure solutions to Euler-alignment/Aw--Rascle--Zhang model of collective behaviour
• Exponential and algebraic decay in Euler--alignment system with nonlocal interaction forces

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