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arXiv · 2503.07345

On the Gross-Pitaevskii evolution linearized around the degree-one vortex

Jonas Luhrmann·Wilhelm Schlag·Sohrab Shahshahani
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Abstract

We study the evolution of the Gross-Pitaevskii equation linearized around the Ginzburg-Landau vortex of degree one under equivariant symmetry. Among the main results of this work, we determine the spectrum of the linearized operator, uncover a remarkable $L^2$-norm growth phenomenon related to a zero-energy resonance, and provide a complete construction of the distorted Fourier transform at small energies. The latter hinges upon a meticulous analysis of the behavior of the resolvent in the upper and lower half-planes in a small disk around zero-energy.

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Jonas Luhrmann, Wilhelm Schlag, Sohrab Shahshahani. 2025-03-10. On the Gross-Pitaevskii evolution linearized around the degree-one vortex. https://arxiv.org/abs/2503.07345

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