From local energy bounds to dimensional estimates in a reduced model for type-I superconductors.

par Michael Goldman (CNRS, LJLL)

mardi 11 oct. 2022, 15:15 → 16:15 Europe/Paris

Fokko du Cloux (Bâtiment Braconnier, La Doua)

In the limit of vanishing but moderate external magnetic field, we 
derived a few years ago together with S. Conti, F. Otto and S. Serfaty 
a branched transport problem from the full Ginzburg-Landau model. In 
this regime, the irrigated measure is the Lebesgue measure and, at 
least in a simplified 2d setting, it is possible to prove that the 
minimizer is a self-similar branching tree. In the regime of even 
smaller magnetic fields, a similar limit problem is expected but this 
time the irrigation of the Lebesgue measure is not imposed as a hard 
constraint but rather as a penalization. While an explicit computation 
of the minimizers seems here out of reach, I will present some ongoing 
project with G. De Philippis and B. Ruffini relating local energy 
bounds to dimensional estimates for the irrigated measure.