Uniqueness of solutions for the Ginzburg-Landau model of superconductivity in three spatial dimensions
This paper is devoted to study the uniqueness of weak solutions to the time-dependent Ginzburg-Landau (TDGL for short) model of superconductivity in three spatial dimensions. Here the author first establishes the \(L^p\) regularity of solutions and then, based on the regularity, shows the uniqueness of weak solutions for the periodic TDGL equations with any \(L^p\) \((p\geq 4)\) initial data. Existence for various \(L^p\) initial data was proved by \textit{S. Wang} and \textit{M.-Q. Zhan} [Nonlinear Anal., Theory Methods Appl. 36 B, No. 6, 661--677 (1999; Zbl 0919.35128)] and the author and \textit{N. Su} [Proc. R. Soc. Edinb., Sect. A, Math. 129, 627--639 (1999; Zbl 0940.35045)].
scientific article; zbMATH DE number 1763692