论文标题
使用Hartree非线性II：动力学的三维波方程的不变吉布斯度量
Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics
论文作者
论文摘要
在这个两纸系列中，我们证明了具有Hartree非线性的三维波方程的Gibbs的不变性。新颖性在于吉布斯（Gibbs）相对于高斯自由场的奇异性。 在本文中，我们关注主要结果的动态方面。局部理论基于一种para控制的方法，该方法结合了分散方程，谐波分析和随机矩阵理论的成分。但是，主要贡献在于全球理论。我们开发了一个新的全球化论点，该论点解决了吉布斯量度及其后果的奇异性。
In this two-paper series, we prove the invariance of the Gibbs measure for a three-dimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a para-controlled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences.
