Stochastic PDEs: from singularity to large scale behavior

• Grant number: 23/08713-8
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• Start date: October 01, 2023
• End date: June 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Paulo Regis Caron Ruffino
• Grantee: Andrey Jhen Shan Chen
• Supervisor: Tommaso Rosati
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Warwick, England
• Associated to the scholarship: 22/00284-8 - Geometry of foliations via foliated Brownian motion, BP.DD

Abstract

Stochastic partial differential equations model physical phenomena in the presence of noise. The exact nature of the noise may vary, leading to a plethora of mathematical tools developed for their treatment. This proposal is built around two lines of research, captured by two conjectures, which are distinct, yet deeply intertwined. Both refer to the 2D stochastic Navier--Stokes equations (SNS) on finite volume: Conjecture 1: SNS exhibits chaos; Conjecture 2: SNS with non-degenerate noise are uniquely ergodic in the full subcritical regime, in the sense of M. Hairer's {\it Theory of regularity structures}, Invent. Math., 2014. (AU)