| Texto completo | |
| Autor(es): |
Simon, Marielle
;
Olivera, Christian
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 253, p. 19-pg., 2024-12-28. |
| Resumo | |
This paper considers a large class of nonlinear integro-differential scalar equations which involve an anomalous diffusion ( e.g. driven by a fractional Laplacian) and a non-local singular convolution kernel. Each of those singular equations is obtained as the macroscopic limit of an interacting particle system modeled as N coupled stochastic differential equations driven by L & eacute;vy processes. In particular we derive quantitative estimates between the microscopic empirical measure of the particle system and the solution to the limit equation in some non- homogeneous Sobolev space. Our result only requires very weak regularity on the interaction kernel, therefore it includes numerous applications, e.g.: the 2 d turbulence model (including the quasi-geostrophic equation) in sub-critical regime, the 2 d generalized Navier-Stokes equation, the fractional Keller-Segel equation in any dimension, and the fractal Burgers equation. (AU) | |
| Processo FAPESP: | 22/03379-0 - Análise estocástica e determinística para modelos irregulares |
| Beneficiário: | Christian Horacio Olivera |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 20/04426-6 - Dinâmica estocástica: aspectos analíticos, geométricos e aplicações |
| Beneficiário: | Paulo Regis Caron Ruffino |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |