一类带调和势的非线性Schrodinger方程组的爆破问题

The Blow-up to a Class of Nonlinear Schrodinger Equations with Harmonic Potential

研究一类带调和势的非线性Schrodinger方程组的初值问题,通过在Sobolev空间中定义能量空间,运用能量方法,建立质量能量守恒律,利用能量函数,得到了只要初值满足一定的条件,该方程组的解在有限时间内爆破。

In this paper, We study a class of nonlinear Schrodinger equations with harmonic potential. By defining energy space in Sobolev space, using energy method, the conservation laws of the mass and the energy are set up. By using energy function, we prove that the solution of the equations with the initial data will blow-up in finite time.