Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems
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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 Schrodinger-Poisson system for a fixed re-scaled Planck constant.
DescriptionAn addendum was attached on August 17, 2006. The authors made the following two corrections: on the sixth line of Theorem 2.1, the expression A∊ ∈ L∞ ([0, T]; Hs (ℝN)) should be replaced by |A∊| - √C ∈ L∞ ([0, T]; Hs (ℝN)). On the fourteenth line of Theorem 2.2, the expression A∊ should be replaced by |A∊| - √C ∈ L∞ ([0, T]; Hs (ℝN)). See last page of this manuscript for details.
CitationLi, H., & Lin, C. K. (2003). Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems. Electronic Journal of Differential Equations, 2003(93), pp. 1-17.
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