Large time behavior and global existence of solution to the bipolar defocusing nonlinear Schrödinger-Poisson system
Authors:
Chengchun Hao and Ling Hsiao
Journal:
Quart. Appl. Math. 62 (2004), 701-710
MSC:
Primary 35Q55; Secondary 35B40, 82D10
DOI:
https://doi.org/10.1090/qam/2104270
MathSciNet review:
MR2104270
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Abstract: In this paper, we study the large time behavior and the existence of globally defined smooth solutions to the Cauchy problem for the bipolar defocusing nonlinear Schrödinger-Poisson system in the space ${\mathbb {R}^{3}}$.
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J. Bergh and J. Löfström, Interpolation spaces, An introduction, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag: Berlin-New York, 1976
F. Brezzi and P. A. Markowich, The three-dimensional Wigner-Poisson problem: existence, uniqueness and approximation, Math. Meth. Appl. Sci., 14, 35-62 (1991)
F. Castella, $L^{2}$ solutions to the Schrödinger-Poisson system: existence, uniqueness, time behaviour, and smoothing effects, Math. Models Methods Appl. Sci., 7(8), 1051-1083 (1997)
A. Jüngel and S. Wang, Convergence of nonlinear Schrödinger-Poisson systems to the compressible Euler equations, Comm. Part. Diff. Eqs. 28, 1005-1022 (2003)
M. Keel and T. Tao, Endpoint Strichartz estimates, Amer. J. Math., 120, 955-980 (1998)
H. L. Li and C. K. Lin, Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems, Electron. J. Diff. Eqns., 2003, No. 93, pp. 1-17 (2003)
P. A. Markowich, G. Rein and G. Wolansky, Existence and nonlinear stability of stationary states of the Schrödinger-Poisson system, J. Statist. Phys., 106(5-6), 1221–1239 (2002)
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B. X. Wang, Large time behavior of solutions for critical and subcritical complex Ginzburg-Landau equations in $H^{1}$, Science in China (Series A), 46(1), 64-74 (2003)
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© Copyright 2004
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