Euler-flocking system with nonlocal dissipation in 1D: periodic entropy solutions

TL;DR

This paper proves the global existence of periodic entropy weak solutions for a 1D hydrodynamic flocking model with nonlocal dissipation, finite total variation initial data, and bounded away from zero density.

Contribution

It establishes the existence of solutions for a nonlocal flocking model with periodic boundary conditions, expanding understanding of such systems.

Findings

Global existence of periodic entropy weak solutions.

Solutions exist for initial data with finite total variation.

Initial density remains bounded away from zero.

Abstract

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in a periodic domain in one-space dimension with linear pressure term. The main result is the global existence of periodic entropy weak solutions, for periodic initial data having finite total variation and initial density bounded away from zero.