6 papers
On the Smoluchowski-Kramers approximation for the hyperbolic linear sigma model and its mean-field limit
Alexander Czernik, Ruoyuan Liu, Shao Liu
We study the hyperbolic linear sigma model, i.e. a system of interacting stochastic damped nonlinear wave equations (SdNLW) with coupled cubic nonlinearities, posed on t…
The Korteweg-de Vries limit for the global dynamics of the Toda lattice
Ruoyuan Liu, Herbert Koch
It has been observed that the dynamics of the Toda lattice can be well described by solutions of the Korteweg-de Vries (KdV) equation in the continuum limit. We show that, under th…
Hyperbolic linear sigma model and its mean-field limit
Ruoyuan Liu, Shao Liu, Tadahiro Oh
We study large limits of the hyperbolic linear sigma model () on the two-dimensional torus , namely, a system of interacting stochastic d…
Large torus limit of global dynamics of the two-dimensional dispersive Anderson model
Ruoyuan Liu, Nikolay Tzvetkov
We continue the study of the two-dimensional dispersive Anderson model (DAM), i.e. the nonlinear Schrödinger equation with multiplicative spatial white noise. For this model, glob…
Existence, uniqueness, and universality of global dynamics for the fractional hyperbolic -model
Ruoyuan Liu, Nikolay Tzvetkov, Yuzhao Wang
We study the fractional -measure (with order ) and the dynamical problem of its canonical stochastic quantization: the three-dimensional stochastic damped fractional…
Global well-posedness of the energy-critical stochastic nonlinear wave equations
Enguerrand Brun, Guopeng Li, Ruoyuan Liu
We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on and $\mathbb{T}…