Basic Mathematical fluid dynamics

• Grant number: 21/09611-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2022
• End date: February 28, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo Martins dos Santos
• Grantee: Lucas Menezes Barreto
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 19/02512-5 - Systems and partial differential equations, AP.TEM

Abstract

Our research project is centered on mathematical formalisms of fluid mechanics. Particularly, we aim to show how the Reynolds Transport Theorem applied for momentum conservation yields the Cauchy equation. Furthermore, we will try to use physical principles to infer the form of the stress tensor for Newtonian fluids. The stress tensor associated with the Cauchy equation will be rearranged in order to obtain two significant fluid mechanics equations: the Navier-Stokes equation and the vorticity equation. (AU)