THE DENSITY OF SUPERCONDUCTIVITY IN THE BULK REGIME

Bernard Helffer (1, 2) , Ayman Kachmar (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 Faculty of Sciences [Lebanese University] | Faculté des Sciences [Université Libanaise]

In the asymptotic limit of a large Ginzburg-Landau parameter, we give a new asymptotic formula for the L 2-norm of the Ginzburg-Landau order parameter. The formula is valid in the bulk regime where the intensity of the applied magnetic field is of the same order as the Ginzburg-Landau parameter and strictly below the second critical field. Our formula complements the celebrated one of Sandier-Serfaty for the L 4-norm.

Mots clés: Superconductivity; bulk regime

Domaines: Mathématiques [math]

Bernard Helffer, Ayman Kachmar. THE DENSITY OF SUPERCONDUCTIVITY IN THE BULK REGIME. Indiana University Mathematics Journal, In press. ⟨hal-01434780⟩