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Ginzburg-Landau equations and stable solutions in a rotational domain. (English) Zbl 0865.35016
The paper deals with the Ginzburg-Landau model, with or without magnetic effect, in the case of a rotational domain in $$\mathbb{R}^3$$. The results are obtained in the case of a bounded and ring-shaped superconductor and when the external magnetic field is absent. This model was proposed in 1950 for describing low-temperature phenomena appearing in superconductivity or superfluids and it was intensively studied by several authors in the last years.
In their main result, the authors prove that the rotational solutions of the Ginzburg-Landau equation exist and are stable, provided the physical parameter is sufficiently large. This means that these solutions are local minimizers of the corresponding Ginzburg-Landau energetic functional. The proof follows from spectral analysis of the linearized equation.

##### MSC:
 35B35 Stability in context of PDEs 35J60 Nonlinear elliptic equations 82D55 Statistical mechanical studies of superconductors
##### Keywords:
stable solution; rotational solutions
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