一类非线性Schrdinger方程爆破解的L^2集中率

The Rate of L^2 Concentration of Blow-up Solutions for a Class of Nonlinear Schrdinger Equations

研究了一类带势的非线性Schr d inger方程iut=-△u-k(x)|u|4/Nu的初值问题,其中k(x)为C1上有界可微函数.利用经典的非线性Schr d inger方程已有的结果,得到了该方程的爆破解在爆破时刻的L2质量集中速率.

In this paper, the initial-value problem of the following Schrtidinger equation is investigated：iut=-△u-k（x）｜u｜^4/Nu,where k（x） is a bounded differentiable function on C^1 . By using the known results of classical nonlinear Schrodinger equations, the rate of the L^2 -mass concentration of the solution at the blow-up time is obtained.