In this talk, I consider the 3-dimensional stochastic damped
fractional nonlinear wave equation (with order α > 1) with a cubic
nonlinearity, also known as the fractional hyperbolic Φ43-model.
In the first part of my talk, I will give a general introduction of Gibbs
measures and the associated dynamical problems. In particular, I will talk
about the idea of using formal invariance of the Gibbs measure to prove
global well-posedness of the fractional hyperbolic Φ43-model. Then,
I will introduce the notion of weak universality for the fractional
hyperbolic Φ43-model.
In the second part of my talk, I will talk about some technical details in
proving global well-posedness and weak universality for the fractional
hyperbolic Φ43 model. When 1 < α ≤ 9/8, the Gibbs measure
is mutually singular with respect to the base Gaussian measure, which
poses additional challenges in both constructing global dynamics and
establishing weak universality. I will mention the techniques and
novelties we used to overcome this issue of singularity.
Some parts of the talk are based on a joint work with Nikolay Tzvetkov
(ENS Lyon) and Yuzhao Wang (University of Birmingham).
