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

We consider the semiclassical Schrödinger–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 compr...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 251; no. 11; pp. 3028 - 3062
Main Author Masaki, Satoshi
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2011
Subjects
Euler–Poisson equations
Schrödinger–Poisson system
Semiclassical analysis
WKB approximation
Semiclassical analysis
Euler–Poisson equations
WKB approximation
Schrödinger–Poisson system
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Summary:We consider the semiclassical Schrödinger–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 + .
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2011.07.030