Work

From Hamiltonian systems to compressible Euler equation driven by additive Hölder noise

Year: 2025

Type: article

Abstract: In this paper, we derive stochastic compressible Euler Equation from a Hamiltonian microscopic dynamics and consider systems of interacting particles with Hölder noise and potential whose range is large 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 compressible Euler equations driven by additive Hölder path(noise), in the limit as the particle number tends to infinity, for a suitable scaling of the interactions. Furthermore, explicit rates for the convergence are obtained in Besov and Triebel–Lizorkin spaces. Our proof is based on the Itô–Wentzell–Kunita formula for Young integral.

Source: Infinite Dimensional Analysis Quantum Probability and Related Topics

DOI: 10.1142/s0219025725500055

Authors: Jesus M. Correa, Juan David Londoño Acevedo, Christian Olivera

Institutions: Universidade Estadual de Campinas (UNICAMP), Universidad Nacional Abierta y a Distancia

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Fundação de Amparo à Pesquisa do Estado de São Paulo, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico

Awards: Stochastic dynamics: analytical and geometrical aspects with applications, G1857510813, G197386623, G29316538, Stochastic and deterministic analysis for irregular models