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arXiv · 0912.1388

Local existence and WKB approximation of solutions to Schrödinger-Poisson system in the two-dimensional whole space

Satoshi Masaki
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Abstract

We consider the Schrödinger-Poisson system in the two-dimensional whole space. A new formula of solutions to the Poisson equation is used. Although the potential term solving the Poisson equation may grow at the spatial infinity, we show the unique existence of a time-local solution for data in the Sobolev spaces by an analysis of a quantum hydrodynamical system via a modified Madelung transform. This method has been used to justify the WKB approximation of solutions to several classes of nonlinear Schrödinger equation in the semiclassical limit.

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Satoshi Masaki. 2009-12-08. Local existence and WKB approximation of solutions to Schrödinger-Poisson system in the two-dimensional whole space. https://arxiv.org/abs/0912.1388

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