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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-23 18:10 |
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Conference: Bucharest University Faculty of Physics 2019 Meeting
Section: Theoretical Physics and Applied Mathematics
Title:
(Un)Solved conjectures about steady Euler flows
Authors:
Radu SLOBODEANU
Affiliation:
University of Bucharest, Faculty of Physics
E-mail
radualexandru.slobodeanu@g.unibuc.ro
Keywords:
steady Euler flow, plasma, magnetic relaxation, topology
Abstract:
We survey recent significant results regarding the topology and geometry of stationary solutions of Euler equations describing perfect (non-relativistc) steady fluids or ideal magnetohydrodynamic equilibria. This include localization property, Kelvin’s conjecture, and Ghrist-Komendarczyk conjecture, the latter being related to the magnetic relaxation process. Few ideas about the proof will be given in each case. A list of open problems and unsolved conjectures (e.g. Grad conjecture) will be presented in the second part of the talk.
References:
[1] Peralta-Salas, Daniel, and Radu Slobodeanu. "Energy Minimizing Beltrami Fields on Sasakian 3-Manifolds." International Mathematics Research Notices.
[2] Peralta-Salas, D. (2016). Selected topics on the topology of ideal fluid flows. International Journal of Geometric Methods in Modern Physics, 13(Supp. 1), 1630012.
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