UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2022-07-01 16:15

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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.