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Topological and geometric methods in fluid dynamics

Grant number: 21/09311-5
Support type:Scholarships in Brazil - Master
Effective date (Start): December 01, 2021
Effective date (End): July 31, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Cristián Andrés Ortiz González
Grantee:Guilherme Ferreira Vasconcelos Júnior
Home 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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