| Full text | |
| Author(s): |
Simon, Marielle
;
Olivera, Christian
Total Authors: 2
|
| Document type: | Journal article |
| Source: | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 253, p. 19-pg., 2024-12-28. |
| Abstract | |
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) | |
| FAPESP's process: | 22/03379-0 - Stochastic and deterministic analysis for irregular models |
| Grantee: | Christian Horacio Olivera |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 20/04426-6 - Stochastic dynamics: analytical and geometrical aspects with applications |
| Grantee: | Paulo Regis Caron Ruffino |
| Support Opportunities: | Research Projects - Thematic Grants |