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arXiv · 2410.12646

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

Manuel del Pino·Rowan Juneman·Monica Musso
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Abstract

We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution $W(x)=w(r)e^{i\theta}$. Using explicit representation formulae for the Fourier modes in $\theta$, 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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Manuel del Pino, Rowan Juneman, Monica Musso. 2024-10-16. Solvability for the Ginzburg-Landau equation linearized at the degree-one vortex. https://arxiv.org/abs/2410.12646

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