Well-posedness of phase-lock equations of superconductivity

In this article we give an affirmative answer to an open question raised in [M. Zhan, Phase-lock equations and its connections to Ginzburg-Landau equations of superconductivity, J. Nonlinear Anal. 42 (2000) 1063-1075]. There, the author introduced the phase-lock equations to model superconductivity phenomena. We showed that the phase-lock equations have unique solutions with L2 initial data for space dimensions n=2,3.