Semiclassical Limit of the Non-linear Schroedinger-Poisson Equation With Subcritical Initial Data
IOWA STATE UNIV AMES DEPT OF MATHEMATICS
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We study the semi-classical limit of the nonlinear Schroedinger-Poisson NLSP equation for initial data of the WKB type. The semi-classical limit in this case is realized in terms of a density-velocity pair governed by the Euler-Poisson equations. Recently we have shown that the isotropic Euler-Poisson equations admit a critical threshold phenomena, where initial data in the sub-critical regime give rise to globally smooth solutions. Consequently, we justify the semi-classical limit for sub-critical NLSP initial data and confirm the validity of the WKB method.
- Theoretical Mathematics
- Fluid Mechanics