  We study the time-dependent Ginzburg--Landau equations in a three-dimensional
curved polyhedron (possibly nonconvex). Compared with the previous works, we
prove existence and uniqueness of a global weak solution based on weaker
regularity of the solution in the presence of edges or corners, where the
magnetic potential may not be in $L^2(0,T;H^1(\Omega)^3)$.
