The Schrödinger equation with spatial white noise potential

2016/12/07 by Debussche, Arnaud, Weber, Hendrik · 6 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1612.02230

Abstract

We consider the linear and nonlinear Schrödinger equation with a spatial white noise as a potential in dimension 2. We prove existence and uniqueness of solutions thanks to a change of unknown originally used in [8] and conserved quantities.

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• Regularization for the Schrödinger equation with rough potential: high-dimensional case
• Regularization for the Schrödinger equation with rough potential: one-dimensional case
• On domains of elliptic operators with distributional coefficients

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