Global Existence and Uniqueness of Helically Symmetric Weak Solutions to the Ginzburg–Landau Model in Superconductivity

Key Points

• The study aims to demonstrate the global existence and uniqueness of helically symmetric weak solutions to the Ginzburg–Landau model in superconductivity.
• Defined helical symmetry using cylindrical coordinates (r,θ,z) and a variable ξ=nθ+αz, with n as an even integer and α>0.
• Applied geometric constraints to reduce the dimensionality of the problem to manage L2 initial conditions.
• Supported the choice of the Lorentz gauge in the model.
• Proved global existence of helically symmetric weak solutions for the Ginzburg–Landau model in R3.
• Established uniqueness of these solutions under L2 initial data.
• Confirmed that the dimension reduction strategy effectively simplifies the analysis of the system.