The study of the singularity problem for incompressible flow through toy models

• Grant number: 18/05899-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2018
• End date: December 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Anne Caroline Bronzi
• Grantee: Leonardo Epiphanio Galvão
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this research project we propose the study of the singularity problem for incompressible flow in dimension three through the analysis of toy models that have analytical and/or geometric properties similar to the equations of interest. At the end of this project the student will have learned about the main open problems in the area of fluid dynamics, as well as some of the classical methods from the theory of partial differential equations such as the De Giorgi method, the barrier method and the use of tools from Harmonic Analysis.