From Stochastic Hamiltonian Systems to Stochastic Compressible Euler Equation

2023/01/19 by Jesus Correa, Correa, Jesus, Christian Olivera +1
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Classical mechanics #Compressibility #Computer science #Euler equations #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Geometric Analysis and Curvature Flows #Hamiltonian (control theory) #Hamiltonian system #Limit (mathematics) #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Mechanics #Norm (philosophy) #Particle system #Physics #Position (finance) #Probability (math.PR) #Range (aeronautics) #Sobolev space #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2301.08101

openalex publication_date 2023/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We study a stochastic Hamiltonian system of N particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical measures associated to the position and velocity of the system converge to the solutions of stochastic compressible Euler equations in the limit as the particle number tends to infinity. Moreover, we quantify the distance between particles and the limit in suitable Sobolev norm.

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