Global solutions to vortex density equations arising from sup-conductivity

Abstract In the first part of this paper, we establish the existence of a global renormalized solution to a family of vortex density equations arising from superconductivity. And we show by an explicit example the necessity of the notion of renormalized solution to be used here. In the second part, we prove the global existence and uniqueness of W 1 , p and C α solutions to a modified model, which is derived from the physically sign-changing vortices case.

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