Flux of superconducting vortices through a domain

This article addresses the mathematical study of a mean-field model of superconducting vortices in a II-type superconductor, previously introduced in [S. J. Chapman, SIAM J. Appl. Math., 55 (1995), pp. 1259-1279]. We investigate a hyperbolic-elliptic type system of PDEs in a given domain. Motivated by physical experiments, we consider nonzero and nonconstant boundary conditions, which describe a flux of superconducting vortices through the domain. We prove the existence of the regular solutions of a parabolic-elliptic approximated system and establish a uniform L-infinity-bound for the vorticity and the convergence to the initial system. Finally, we analyze the regularity of weak solutions.