Work

Solvability for the Ginzburg-Landau equation linearized at the degree-one vortex

Year: 2025

Type: article

Abstract: We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution W ( x ) = w ( r ) e i θ . Using explicit representation formulae for the Fourier modes in θ , we obtain sharp estimates for the inverse of the linearized operator which hold for a large class of right-hand sides. This theory can be applied, for example, to estimate the inverse after dropping the usual orthogonality conditions.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.111105

Authors: Manuel del Pino, Rowan Juneman, Monica Musso

Institution: University of Bath

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250