Modern methods in differential geometry and geometric analysis
Geometry of control systems, dynamical and stochastics systems
Numerical investigation on autonomous underwater vehicle hydrodynamics
Grant number: | 21/09311-5 |
Support Opportunities: | Scholarships in Brazil - Master |
Start date: | December 01, 2021 |
End date: | October 16, 2022 |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
Principal Investigator: | Cristián Andrés Ortiz González |
Grantee: | Guilherme Ferreira Vasconcelos Júnior |
Host Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
Abstract This master project studies the necessary geometric concepts to understand a theorem by Arnold on the geodesic formulation of Euler equations describing an incompressible fluid. The main goal of the project consists on studying recent results by Izosimov and Khesin in which Arnolds strategy is generalized to the setting of Lie groupoids equipped with an invariant Riemannian metric. Such an extension allows one to use techniques from geometric and topological hydrodynamics to describe fluids whose velocity has singularities known as vortex sheets. (AU) | |
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