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Hydrodynamic limit of the Gross-Pitaevskii equation by Jerrard, Robert L.; Spirn, Daniel is a scholarly article available to read on EtoBox.

What is Hydrodynamic limit of the Gross-Pitaevskii equation about?

We study dynamics of vortices in solutions of the Gross-Pitaevskii equation $i \partial_t u = \Delta u + \varepsilon^{-2} u (1 - |u|^2)$ 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].

Author

Jerrard, Robert L.; Spirn, Daniel

Published

2013

Language

EN