Giorgi, T.; Phillips, D. The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model. (English) Zbl 1094.82021 SIAM Rev. 44, No. 2, 237-256 (2002). Summary: We study the behavior of a superconducting material subjected to a constant applied magnetic field, \(\mathbf H_a=h\mathbf e\) with \(| \mathbf e| =1\), using the Ginzburg-Landau theory. We analytically show the existence of a critical field \(\bar h,\) for which, when \(h>\bar h,\) the normal states are the only solutions to the Ginzburg-Landau equations. We estimate \(\bar h\). As \(\kappa\downarrow 0\) we derive \(\bar h=O(1)\), while as \(\kappa\to\infty\) we obtain \(\bar h=O(\kappa)\). Cited in 5 Documents MSC: 82D55 Statistical mechanics of superconductors 35Q55 NLS equations (nonlinear Schrödinger equations) 35A15 Variational methods applied to PDEs 35Q60 PDEs in connection with optics and electromagnetic theory Keywords:superconductivity; Ginzburg-Landau equations; upper critical fields; normal state PDFBibTeX XMLCite \textit{T. Giorgi} and \textit{D. Phillips}, SIAM Rev. 44, No. 2, 237--256 (2002; Zbl 1094.82021) Full Text: DOI