论文标题
均匀磁场中的非线性schrödinger方程
Non-linear Schrödinger Equation in a uniform magnetic field
论文作者
论文摘要
本文的目的是在2和3的维度上研究具有外部均匀磁场的纯式非线性schrödinger方程。特别是，我们得出了关于初始数据和非线性功率的一般标准，因此相应的解决方案在有限的时间内爆炸，并且我们表明，随着磁场强度的增加，爆破的时间减少了。此外，我们还讨论了有关Mehler内核2个维度的Strichartz估计值的一些观察结果，以及非线性Pauli方程的类似爆炸结果。
The aim of this paper is to study, in dimensions 2 and 3, the pure-power non-linear Schrödinger equation with an external uniform magnetic field included. In particular, we derive a general criteria on the initial data and the power of the non-linearity so that the corresponding solution blows up in finite time, and we show that the time for blow up to occur decreases as the strength of the magnetic field increases. In addition, we also discuss some observations about Strichartz estimates in 2 dimensions for the Mehler kernel, as well as similar blow-up results for the non-linear Pauli equation.
