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

作者：Masaki Satoshi^*

来源：Journal of Differential Equations, 2011, 251(11): 3028-3062.

DOI：10.1016/j.jde.2011.07.030

• Semiclassical analysis
• WKB approximation
• Schrodinger-Poisson system
• Euler-Poisson equations

We consider the semiclassical Schrodinger-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(+).

• 出版日期2011-12-1