arXiv subjects

Jesus Correa

Publications and source records attributed to Jesus Correa.

3 recordsLinked to original sources

arXiv2024

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

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.

math.AP↗

arXiv2023

From Hamiltonian Systems to Compressible Euler Equation driven by additive H\"older noise

We derive stochastic compressible Euler Equation from a Hamiltonian microscopic dynamics. We consider systems of interacting particles with H\"older 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 H\"older 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 It\^o-Wentzell-Kunita formula for Young integral.

math.AP↗

arXiv2023

From Stochastic Hamiltonian Systems to Stochastic Compressible Euler Equation

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.

math.AP↗