Stochastic forcing in hydrodynamic models with non-local interactions

TL;DR

This paper proves the existence of solutions for a stochastic hydrodynamical model that describes collective animal behavior with non-local interactions and noise, laying groundwork for further analysis.

Contribution

It establishes the existence of dissipative martingale solutions for a stochastic Euler system with non-local forces and noise, a novel result in this context.

Findings

Existence of dissipative martingale solutions proven

Framework for analyzing stochastic collective behavior models

Foundation for future stochastic analysis of non-local hydrodynamics

Abstract

The hydrodynamical model of the collective behavior of animals consists of the Euler equation with additional non-local forcing terms representing the repulsive and attractive forces among individuals. This paper deals with the system endowed with an additional white-noise forcing and an artificial viscous term. We provide a proof of the existence of a dissipative martingale solution -- a cornerstone for a subsequent analysis of the system with stochastic forcing.