Abstract:

The two-dimensional Ginzburg-Landau (GL) model with a magnetic field holds significant importance in physics and considerable interest in mathematics. In this paper, we examine two distinct types of GL models: one describing thin-film superconductors and the other modeling rotating superfluids. First, we compare the corresponding energy functionals and demonstrate that they become comparable when the GL parameter $\lambda$ is sufficiently large. Subsequently, we further investigate the minimization problem for the energy functional associated with rotating superfluids over an annular domain with a fixed-degree boundary condition. Our analysis reveals that the boundary degree condition influences the existence of minimizers when the GL parameter is large.

Key words: elliptic equations, minimization problems with constraints, variational methods for elliptic equaitons