2025/10/16 by Carlos Román, Román, Carlos, Étienne Sandier +3 · 1 citation
Physics and Astronomy · #35J50 #35Q56 #49K10 #82D55 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Ionosphere and magnetosphere dynamics #Magnetic confinement fusion research #Mathematical Physics (math-ph) #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.2510.14910
openalex created_date 2025/10/13 · openalex publication_date 2025/10/16 · openalex updated_date 2026/07/28
We complete our study of the three dimensional Ginzburg--Landau functional with magnetic field, in the asymptotic regime of a small inverse Ginzburg--Landau parameter ε, and near the first critical field Hc1 for which the first vortex filaments appear in energy minimizers. Under a nondegeneracy condition, we show a next order asymptotic expansion of Hc1 as ε → 0, and exhibit a sequence of transitions, with vortex lines appearing one by one as the intensity of the applied magnetic field is increased: passing Hc1 there is one vortex, then increasing Hc1 by an increment of order log |logε| a second vortex line appears, etc. These vortex lines accumulate near a special curve Γ0, solution to an isoflux problem. We derive a next order energy that the vortex lines must minimize in the asymptotic limit, after a suitable horizontal blow-up around Γ0. This energy is the sum of terms where penalizations of the length of the lines, logarithmic repulsion between the lines and magnetic confinement near Γ0 compete. This elucidates the shape of vortex lines in superconductors.