Estimates for the Gross-Pitaevskii equation linearized around a vortex
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∞ and boundedness in L2 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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