Global well-posedness of the time-dependent Ginzburg-Landau superconductivity model in curved polyhedra

We prove global existence and uniqueness of weak solutions for the time-dependent Ginzburg-Landau equations in a three-dimensional curved polyhedron which is not necessarily convex, where the gradient of the magnetic potential may not be square integrable. Preceding analyses all required the gradient of the solution to be square integrable, which is only true in convex or smooth domains.