Weak solutions to the Ginzburg-Landau model in superconductivity with the temporal gauge

Abstract

We first prove the uniqueness of weak solutions to the 3-D Ginzburg-Landau system in superconductivity with the temporal gauge if , which is a critical space for some positive constant . We also prove the global existence of solutions for the Ginzburg-Landau system with magnetic diffusivity or . Finally, we prove the uniform bounds with respect to of strong solutions in space dimensions . Consequently, the existence of the limit as can be established.

Keywords:

• Uniqueness
• weak solutions
• superconductivity
• temporal gauge

AMS Subject Classifications:

• 35A05
• 35A40
• 82D55

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

J. Fan is partially supported by NSFC [grant number 11171154].