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arXiv · 2511.17063

Local wellposedness of the 2d Anderson-Gross-Pitaevskii equation

Samaël Mackowiak
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Abstract

In this paper, the local wellposedness of a general Gross-Pitaevskii equation with rough potential is proven in dimension 2. The class of rough potentials we are considering is large enough to contain the spatial white noise and thus a renormalization procedure may be needed. We first construct the associated Schr\"odinger operator from its quadratic form. Then, the regularity of elements of its domain is explored. This allows to use a paracontrolled approach in order to obtain Strichartz estimates, which are used to prove the local wellposedness by a contraction argument.

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Samaël Mackowiak. 2025-11-21. Local wellposedness of the 2d Anderson-Gross-Pitaevskii equation. https://arxiv.org/abs/2511.17063

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