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Stable solutions of the Ginzburg-Landau equation with magnetic field. (Solutions stables de l’équation de Ginzburg-Landau en présence de champ magnétique.) (French. Abridged English version) Zbl 0913.35134

Summary: We study the Ginzburg-Landau equation near the first critical value of the magnetic field \(H_{c_1}\). We prove an estimate of this value, and we find branches of stable solutions of the equation for which we show that vortices appear while passing \(H_{c_1}\).

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
82D55 Statistical mechanics of superconductors
35R35 Free boundary problems for PDEs
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