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

2025/11/21 by Samaël Mackowiak, Mackowiak, Samaël · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.2511.17063

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 Schrödinger 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.

Citations

• A simple construction of the Anderson operator via its quadratic form in dimensions two and three
• Anderson Hamiltonian and associated Nonlinear Stochastic Wave and Schrödinger equations in the full space
• Analysis of the Anderson operator
• 2D random magnetic Laplacian with white noise magnetic field
• Weyl law for the Anderson Hamiltonian on a two-dimensional manifold
• Two dimensional nonlinear Schrödinger equation with spatial white noise potential and fourth order nonlinearity
• The Schrödinger equation with spatial white noise potential
• The continuous Anderson hamiltonian in dimension two
• Sobolev spaces associated to the harmonic oscillator
• On One-Parameter Unitary Groups in Hilbert Space

Cited by

• Standing waves of the Anderson-Gross-Pitaevskii equation

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