Radial solutions for the Ginzburg-Landau equation with applied magnetic field.
The author considers a superconducting cylinder with applied magnetic field parallel to its axis. At a macroscopic level, the situation depends on three parameters in \(\mathbb{R}_+\): \(\kappa\) material constant, \(r\) the radius of the cylinder, and \(h\) the intensity of the applied magnetic field. This paper deals with a systematic study of symmetric vortices for the Ginzburg-Landau model. The paper consists of two main parts. The first one is devoted to the existence, characterization and general properties of symmetric vortices. The author proves that for all parameters \((\kappa,r,h)\) there exists a symmetric vortex \((\psi,A)\) of any degree \(d\geq 2\) satisfying the boundary conditions \(\psi|_{\partial B_r}= e^{id\theta}\), \(\text{curl}(A)|_{\partial B_r}= he_3\). The second part of this work is devoted to the computation of boundary values from the initial data \((\alpha, c)\), and vice versa. Moreover, the author studies more accurately the asymptotic behaviour on the limiting branch as the parameter \(\alpha\) grows to infinity.
Ginzburg-Landau model of superconductivity
scientific article; zbMATH DE number 2032558