Large time WKB approximation for multi-dimensional semiclassical Schrödinger-Poisson system |
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Authors: | Satoshi Masaki |
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Institution: | Division of Mathematics, Graduate School of Information Sciences, Tohoku University, Aza-aoba 6-3-09, Aramaki, Aoba-ku, Sendai 980-8579, Japan |
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Abstract: | 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+. |
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Keywords: | Semiclassical analysis WKB approximation Schrö dinger-Poisson system Euler-Poisson equations |
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