Global well-posedness of the time-dependent Ginzburg-Landau   superconductivity model in curved polyhedra
  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 $L^2(0,T;H^1(\Omega)^3)$. 
Buyang Li and Chaoxia Yang
math.AP