Semiclassical Limit of the Nonlinear Schrödinger-Poisson Equation with Subcritical Initial Data
Semiclassical Limit of the Nonlinear Schrödinger-Poisson Equation with Subcritical Initial Data
复制标题
亚临界初始数据非线性薛定谔-泊松方程的半经典极限
DOI：
10.4310/maa.2002.v9.n4.a3
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发表时间：
2002
影响因子：
0.3
通讯作者：
E. Tadmor
中科院分区：
文献类型：
--
作者：
Hailiang Liu;E. Tadmor
研究了WKB型初始数据下非线性薛定谔-泊松方程的半经典极限。这种情况下的半经典极限是用由欧拉-泊松方程控制的密度-速度对来实现的。最近我们在印第安纳大学的英语数学课上展示过。J., 50(2001), 109-157)，各向同性欧拉-泊松方程承认临界阈值现象，其中亚临界区域的初始数据产生全局光滑解。因此，我们证明了亚临界NLSP初始数据的半经典极限，并证实了WKB方法的有效性。
We study the semi-classical limit of the nonlinear Schrodinger-Poisson (NLSP) equa- tion 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 in (ELT, Indiana Univ. Math. J., 50 (2001), 109-157), 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.