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arXiv · 1310.4558

Hydrodynamic limit of the Gross-Pitaevskii equation

Robert L. Jerrard·Daniel Spirn
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Abstract

We study dynamics of vortices in solutions of the Gross-Pitaevskii equation $i \partial_t u = Δu + \varepsilon^{-2} u (1 - |u|^2)$ on $\mathbb{R}^2$ with nonzero degree at infinity. We prove that vortices move according to the classical Kirchhoff-Onsager ODE for a small but finite coupling parameter $\varepsilon$. By carefully tracking errors we allow for asymptotically large numbers of vortices, and this lets us connect the Gross-Pitaevskii equation on the plane to two dimensional incompressible Euler equations through the work of Schochet [21].

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Robert L. Jerrard, Daniel Spirn. 2013-10-17. Hydrodynamic limit of the Gross-Pitaevskii equation. https://arxiv.org/abs/1310.4558

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