| Abstract: |
| The Gross-Pitaevskii equation in the plane arises as a physical model for an idealized, two-dimensional superfluid. We construct solutions to this equation with multiple vortices of degree \(\pm1\), corresponding to concentration points of the associated fluid vorticity. The vortex dynamics is described on any finite time interval, and at leading order is governed by the classical Helmholtz-Kirchhoff system. Compared to previous rigorous results of Bethuel-Jerrard-Smets and Jerrard-Spirn, we use a different method based on linearization around an approximate solution. This approach provides a very precise description of the solutions near the vortex set and information on lower order corrections to the vortex dynamics. Moreover, our analysis of the linearized problem is potentially of independent interest in the study of long-time dynamics. This is joint work with Manuel del Pino and Monica Musso. |
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