Pré-Publication, Document De Travail Année : 2006

A remark on the Cauchy Problem for the 2D Gross-Pitaevskii equation with non zero degree at infinity

Fabrice Bethuel
Didier Smets

Résumé

We prove global well-posedness for the Gross-Pitaevskii equation on the plane for classes of initial data having non zero topological degree at infinity and therefore infinite Ginzburg-Landau energy. These classes allow to consider arbitrary configurations of vortices as initial data. Our work follows recent results of Patrick Gérard [9] and Clément Gallo [4] where the finite energy regime is treated.

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hal-00121718 , version 1 (21-12-2006)

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  • HAL Id : hal-00121718 , version 1

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Fabrice Bethuel, Didier Smets. A remark on the Cauchy Problem for the 2D Gross-Pitaevskii equation with non zero degree at infinity. 2006. ⟨hal-00121718⟩
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