Seminario EDP UAM-ICMAT
Asymmetry of principle curl eigenfunctions in rotationally symmetric domains
Ponente: David Perrella (ICMAT)Fecha: viernes 21 de noviembre de 2025 - 11:30Lugar: Aula Naranja, ICMAT
Resumen:
In the late 50s Woltjer proposed the idea that magnetic fields in astrophysical plasmas tend to relax so as to minimise their energy while conserving a quantity known as helicity - the average linking between pairs of magnetic field lines. Later in the 70s, Taylor applied this idea to other contexts, such as laboratory plasmas where these magnetic fields get the name taylor states. The variational problem of minimising L2 energy while keeping helicity fixed is known to have minimisers which are certain principle eigenfields of the curl operator. These eigenfields live in a domain of the curl for which its inverse is compact and self-adjoint.
This talk will be on recent joint work with Peralta-Salas (ICMAT) and Pfefferlé (University of Western Australia) on the construction of rotationally symmetric toroidal domains for which
(i) principle curl eigenspace is simple so that all principle eigenfields are symmetric, and
(ii) others for which no minimiser is symmetric.
This serves as another counterexample to the folk wisdom that “principal eigenfields must inherit the symmetries of the domain" and demonstrates a stark contrast between the curl operator and the Laplacian on functions.
