Juan Londoño | Searcharxiv

arXiv2025

From Hamiltonian Systems to Compressible Euler Equation driven by additive Hölder noise

We derive stochastic compressible Euler Equation from a Hamiltonian microscopic dynamics. We consider systems of interacting particles with Hölder noise and 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 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.

math.AP↗

arXiv2023

Euler-Lagrangian approach to stochastic Euler equations in Sobolev Spaces

The purpose of this paper is to establish the equivalence between Lagrangian and classical formulations for the stochastic incompressible Euler equations, the proof is based in Ito-Wentzell-Kunita formula and stochastic analysis techniques. Moreover, we prove a local existence result for the Lagrangian formulation in suitable Sobolev Spaces.

math.AP↗