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Stochastic PDEs: from singularity to large scale behavior

Grant number: 23/08713-8
Support Opportunities:Scholarships abroad - Research Internship - Doctorate (Direct)
Effective date (Start): October 01, 2023
Effective date (End): 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
Research place: 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)

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