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

Manuel Del Pino; Rowan Juneman; Monica Musso

doi:10.1016/j.jfa.2025.111105

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

Manuel Del Pino, Rowan Juneman, Monica Musso

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution W (x) = w (r) eⁱ^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.

Original language	English
Article number	111105
Journal	Journal of Functional Analysis
Volume	289
Issue number	9
Early online date	18 Jun 2025
DOIs	https://doi.org/10.1016/j.jfa.2025.111105
Publication status	Published - 1 Nov 2025

Data Availability Statement

No data was used for the research described in the article.

Funding

M. del Pino has been supported by the Royal Society Research Professorship grant RP-R1-180114 and by the ERC/UKRI Horizon Europe grant ASYMEVOL, EP/Z000394/1 . R. Juneman has been supported by a University Research Studentship at the University of Bath .

Funders	Funder number
University of Bath
European Research Council
Royal Society	RP-R1-180114
EU - Horizon 2020	EP/Z000394/1

Keywords

Degree-one vortex
Ginzburg-Landau equation
Linearized operator

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2025.111105Licence: CC BY

Cite this

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abstract = "We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution W (x) = w (r) eiθ. 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.",

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N2 - We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution W (x) = w (r) eiθ. 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.

AB - We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution W (x) = w (r) eiθ. 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.

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KW - Linearized operator

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

Abstract

Data Availability Statement

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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