Abstract
This paper concerns the well-posedness and semiclassical limit of nonlinear Schrödinger-Poisson systems. We show the local well-posedness and the existence of semiclassical limit of the two models for initial data with Sobolev regularity, before shocks appear in the limit system. We establish the existence of a global solution and show the time-asymptotic behavior of a classical solutions of Schrödinger-Poisson system for a fixed re-scaled Planck constant.
| Original language | English |
|---|---|
| Pages (from-to) | 1-17 |
| Number of pages | 17 |
| Journal | Electronic Journal of Differential Equations |
| Volume | 2003 |
| Publication status | Published - 8 Sept 2003 |
| Externally published | Yes |
Keywords
- Euler-Poisson system
- Quantum hydrodynamics
- Quasilinear symmetric hyperbolic system
- Schrödinger-Poisson system
- Semiclassical limit
- WKB expansion