Global solutions to vortex density equations arising from sup-conductivity

  • Nader Masmoudi

    Courant Institute, New York University, New York, NY 10012, USA
  • Ping Zhang

    Academy of Mathematics & System Sciences, CAS, Beijing 100080, China


In the first part of this paper, we establish the existence of a global renormalized solution to a family of vortex density equations arising from superconductivity. And we show by an explicit example the necessity of the notion of renormalized solution to be used here. In the second part, we prove the global existence and uniqueness of and solutions to a modified model, which is derived from the physically sign-changing vortices case.


On montre l'existence de solutions globales pour une famille d'équations provenant de la super-conductivité. On montre par un exemple que la notion de solutions renormalizées est nécessaire ici. Dans la seconde partie de ce papier, on montre l'existence et l'unicité de solutions et pour un modèle qui décrit des vortex qui changent de signes.

Cite this article

Nader Masmoudi, Ping Zhang, Global solutions to vortex density equations arising from sup-conductivity. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 4, pp. 441–458

DOI 10.1016/J.ANIHPC.2004.07.002