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

Autor(es)

Correa, Jesus M. ; Acevedo, Juan David Londono ; Olivera, Christian

• Tipo de documento: Artigo Científico
• Fonte: INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS; v. N/A, p. 18-pg., 2025-04-05.

Resumo

In this paper, we derive stochastic compressible Euler Equation from a Hamiltonian microscopic dynamics and consider systems of interacting particles with Holder 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 Holder 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 & ocirc;-Wentzell-Kunita formula for Young integral. (AU)

• Processo FAPESP: 20/04426-6 - Dinâmica estocástica: aspectos analíticos, geométricos e aplicações
• Beneficiário: Paulo Regis Caron Ruffino
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 22/03379-0 - Análise estocástica e determinística para modelos irregulares
• Beneficiário: Christian Horacio Olivera
• Modalidade de apoio: Auxílio à Pesquisa - Regular