Existence, regularity, and asymptotic behaviour of the solutions to the Ginzburg-Landau equations on \({\mathbb{R}}^ 3\)
The paper is devoted to the study of the solutions of the Ginzburg-Landau equation in \(R^ 3\). The existence of regular solutions of this equation is proved in the presence of an arbitrary distributed external magnetic field. The solutions found are in the Coulomb gauge and stay at the lowest energy level (ground state). It is shown that these solutions are energetically stable. If the external field is sufficiently regular then the solutions are shown to have good decaying asymptotics.
scientific article; zbMATH DE number 4111219
scientific article