Differential equations with fractional derivatives and their applications
Numerical analysis and mathematical modeling of non-linear PDEs applied to fluid d...
| 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 |
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) | |
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