Asymptotic limit of nonlinear Schrödinger-Poisson system withgeneral initial data
Asymptotic limit of nonlinear Schrödinger-Poisson system withgeneral initial data
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DOI：
10.3934/krm.2011.4.767
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发表时间：
2011-08
影响因子：
1
通讯作者：
Q. Ju;Fucai Li;Hai-liang Li
中科院分区：
文献类型：
--
作者：
Q. Ju;Fucai Li;Hai-liang Li
研究了具有一般WKB初始数据的非线性薛定谔-泊松系统的渐近极限。证明了当普朗克常数$\hbar$和德拜长度$\lambda$都趋于零时，由非线性薛定谔-泊松系统的光滑解定义的电流收敛于不可压缩欧拉方程加上快速奇异振荡梯度矢量场项的强解。证明涉及均质化技术、对称拟线性双曲系统理论和椭圆估计，关键是建立关于普朗克常数和德拜长度的一致有界估计。
The asymptotic limit of the nonlinear Schrodinger-Poisson system with general WKB initial data is studied in this paper. It is proved that the current, defined by the smooth solution of the nonlinear Schrodinger-Poisson system, converges to the strong solution of the incompressible Euler equations plus a term of fast singular oscillating gradient vector fields when both the Planck constant $\hbar$ and the Debye length $\lambda$ tend to zero. The proof involves homogenization techniques, theories of symmetric quasilinear hyperbolic system and elliptic estimates, and the key point is to establish the uniformly bounded estimates with respect to both the Planck constant and the Debye length.