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arXiv · 2503.02953

Estimates for the Gross-Pitaevskii equation linearized around a vortex

Charles Collot·Pierre Germain·Eliot Pacherie
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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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Charles Collot, Pierre Germain, Eliot Pacherie. 2025-03-04. Estimates for the Gross-Pitaevskii equation linearized around a vortex. https://arxiv.org/abs/2503.02953

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