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Estimates for the Gross-Pitaevskii equation linearized around a vortex

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arxiv 2503.02953 v3 pith:I3B2VR5F submitted 2025-03-04 math.AP

Charles Collot , Pierre Germain , Eliot Pacherie This is my paper · ORCID
classification math.AP
keywords linearizedaroundequationestimatesgross-pitaevskiivortexanalysisassociated
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abstract

We consider the linearized two-dimensional Gross-Pitaevskii equation around a vortex of degree one, with data in the same equivariance class. Various estimates are proved for the solution; in particular, conditions for optimal decay in $L^\infty$ and boundedness in $L^2$ are identified. The analysis relies on a full description of the spectral resolution of the linearized operator through the associated distorted Fourier transform.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Asymptotic stability of the degree-one vortex in the abelian Yang-Mills-Higgs model: Spectral Theory and Numerics

    math.AP 2026-08 conditional novelty 7.0 of 10

    Certified spectral analysis and numerics prove the degree-one vortex linearized operator has one internal mode with eigenvalue in [0.777471875,0.77747375] and negative Fermi Golden Rule coefficients.

  2. Nondegeneracy and Morse Index of Ginzburg--Landau Vortices

    math.AP 2026-08 conditional novelty 7.0 of 10

    For Ginzburg-Landau vortices of degree 2 and 3, the only bounded zero modes are the three geometric symmetries, and the Morse indices are 2 and 6.

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