Inviscid limit for the compressible Euler system with non-local interactions

TL;DR

This paper studies the inviscid limit of a viscous approximation to a generalized compressible Euler system with non-local interactions, showing convergence of solutions as viscosity approaches zero under certain conditions.

Contribution

It demonstrates the convergence of dissipative measure-valued solutions to strong solutions of the Euler system in the inviscid limit, extending understanding of non-local interaction models.

Findings

Dissipative measure-valued solutions tend to strong solutions as viscosity vanishes.

The analysis applies to a generalized Euler system with non-local interactions.

Results provide insight into the inviscid limit for models of collective animal behavior.

Abstract

The collective behavior of animals can be modeled by a system of equations of continuum mechanics endowed with extra terms describing repulsive and attractive forces between the individuals. This system can be viewed as a generalization of the compressible Euler equations with all of its unpleasant consequences, e.g., the non-uniqueness of solutions. In this paper, we analyze the equations describing a viscous approximation of a generalized compressible Euler system and we show that its dissipative measure-valued solutions tend to a strong solution of the Euler system as viscosity tends to 0, provided that the strong solution exists.