Ruoyuan Liu - Global dynamics and weak universality for the fractional hyperbolic Phi^4_3 model

by Ruoyuan Liu (The University of Edinburgh)

Monday Dec 2, 2024, 1:00 PM → 3:15 PM Europe/Paris

435 (UMPA, ENS de Lyon)

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).