Semiclassical Limit of the Nonlinear Schr$#x00F6;dinger-Poisson Equation with Subcritical Initial Data
Liu, Hailiang ; Tadmor, Eitan
Methods Appl. Anal., Tome 9 (2002) no. 3, p. 517-532 / Harvested from Project Euclid
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We study the semi-classical limit of the nonlinear Schr$#x00F6;dinger-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.
Publié le : 2002-12-15
Classification:  
@article{1251832422,
     author = {Liu, Hailiang and Tadmor, Eitan},
     title = {Semiclassical Limit of the Nonlinear Schr$\#x00F6;dinger-Poisson Equation with Subcritical Initial Data},
     journal = {Methods Appl. Anal.},
     volume = {9},
     number = {3},
     year = {2002},
     pages = { 517-532},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1251832422}
}

Liu, Hailiang; Tadmor, Eitan. Semiclassical Limit of the Nonlinear Schr$#x00F6;dinger-Poisson Equation with Subcritical Initial Data. Methods Appl. Anal., Tome 9 (2002) no. 3, pp.  517-532. http://gdmltest.u-ga.fr/item/1251832422/