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Basic Mathematical fluid dynamics

Grant number: 21/09611-9
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): March 01, 2022
Effective date (End): February 28, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Marcelo Martins dos Santos
Grantee:Lucas Menezes Barreto
Home 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


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)

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