论文标题
将吉布斯的措施集中在具有谐波潜力的措施
Focusing Gibbs measures with harmonic potential
论文作者
论文摘要
在本文中，我们研究了与聚焦非线性schrödinger方程相关的吉布斯措施，并在欧几里得空间上具有谐波潜力。我们在一维情况下建立了用于正常化的二分法，而在较高维度的情况下，我们在径向假设下建立了二分法。特别是，我们在Burq-thomann-tzvetkov（2005）在Dimension One和Deng（2013）（2013年）中以径向假设的尺寸启动的谐波潜力（2005年）启动的谐波潜力完成了构建Gibbs测量的程序。
In this paper, we study the Gibbs measures associated to the focusing nonlinear Schrödinger equation with harmonic potential on Euclidean spaces. We establish a dichotomy for normalizability vs non-normalizability in the one dimensional case, and under radial assumption in the higher dimensional cases. In particular, we complete the programs of constructing Gibbs measures in the presence of a harmonic potential initiated by Burq-Thomann-Tzvetkov (2005) in dimension one and Deng (2013) in dimension two with radial assumption.
