Large time WKB approximation for multi-dimensional semiclassical Schrödinger-Poisson system

Details Large time WKB approximation for multi-dimensional semiclassical Schrödinger-Poisson system Large time WKB approximation for multi-dimensional semiclassical Schrödinger-Poisson system

2009-06-12

arxiv.org/abs/0906.2296v1

Mathematics

Analysis of PDEs

33 pages

Scientific paper

We consider the semiclassical Schr\"odinger-Poisson system with a special initial data of WKB type such that the solution of the limiting hydrodynamical equation becomes time-global in dimensions at least three. We give an example of such initial data in the focusing case via the analysis of the compressible Euler-Poisson equations. This example is a large data with radial symmetry, and is beyond the reach of the previous results because the phase part decays too slowly. Extending previous results in this direction, we justify the WKB approximation of the solution with this data for an arbitrarily large interval of $\R_+$.

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