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

TL;DR

This paper proves the existence and uniqueness of global weak solutions for the time-dependent Ginzburg-Landau equations in three-dimensional curved polyhedra, including nonconvex cases with edges or corners, under weaker regularity assumptions.

Contribution

It extends previous results by establishing well-posedness of the model in complex geometries with less regularity requirements.

Findings

Proved global existence of weak solutions.

Established uniqueness of solutions.

Handled nonconvex polyhedral domains with edges or corners.

Abstract

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 $L^2(0,T;H^1(\Omega)^3)$.