带逆平方势的非线性Schr?dinger方程的有限时间性态

在关于非相对论分子物理中磁性粒子捕获电子的研究中,带逆平方势的非线性Schr?dinger方程起着重要的作用.我们重点关注该系统有限时间内的存在性和性态,并导出了该系统解爆破的一个显示精确门槛标准.进一步,证明了该系统径对称爆破解的集中性.

Finite Time Behaviour of Nonlinear Schrödinger Equation with Inverse Square Potential

Nonlinear Schrödinger equation with an inverse square potential plays a very important role in the study of electron capture by polar molecules in nonrelativistic molecular physics. We especially focus on the existence and the qualitative behavior of the finite time solution for this system. We first establish an explicit and exact threshold criterion of the blowup solutions, then show the concentration of the radially symmetric blowup solutions.