From particle systems to the stochastic compressible Navier-Stokes equations of a barotropic fluid

2024/01/31 by Correa, Jesus, Olivera, Christian
Earth and Planetary Sciences · Engineering · #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Enhanced Oil Recovery Techniques #FOS: Mathematics #Reservoir Engineering and Simulation Methods

paper · pdf · doi:10.48550/arxiv.2401.17995

openalex publication_date 2024/01/31 · openalex created_date 2024/02/02 · openalex updated_date 2026/07/28

Abstract

We propose a mathematical derivation of stochastic compressible Navier-Stokes equation. We consider many-particle systems with a Hamiltonian dynamics supplemented by a friction term and environmental noise. Both the interaction potential and the additional friction force are supposed to be long range in comparison with the typical distance between neighboring particles. It is shown that the empirical measures associated to the position and velocity of the system converge to the solutions of the stochastic compressible Navier-Stokes equations of a barotropic fluid. Moreover, we quantify the distance between particles and the limit in suitable in Besov and Triebel-Lizorkin spaces.

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