Energy solution to Schrödinger-Poisson system in the two-dimensional whole space

Details Energy solution to Schrödinger-Poisson system in the two-dimensional whole space Energy solution to Schrödinger-Poisson system in the two-dimensional whole space

2010-01-25

arxiv.org/abs/1001.4308v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

We consider the Cauchy problem of the two-dimensional Schr\"odinger-Poisson system in the energy class. Though the Newtonian potential diverges at the spatial infinity in the logarithmic order, global well-posedness is proven in both defocusing and focusing cases. The key is a decomposition of the nonlinearity into a sum of the linear logarithmic potential and a good remainder, which enables us to apply the perturbation method. Our argument can be adapted to the one-dimensional problem.

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