Mean filed limit for partial diferential equations with rough noise

• Grant number: 24/06348-3
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: September 01, 2024
• End date: July 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Christian Horacio Olivera
• Grantee: Simón Hernán Chony Acosta
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 20/04426-6 - Stochastic dynamics: analytical and geometrical aspects with applications, AP.TEM

Abstract

The proposed research work consists of studying certain types of irregular models represented by partial differential equations with roughnoise. One of the main objectives is to obtain quantitative estimates toapproximate, using particle systems, irregular models represented bypartial differential equations with rough noise. Also, we will study existence and uniqueness of these equations in Besov and Triebel-Lizorkinspaces. Some examples are the Keller-Segel systems and the NavierStokes equations.