1 citations · 3 across the 15 of their papers we have counts for
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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…
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, globa…
Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus
Andreia Chapouto, Guopeng Li, Ruoyuan Liu
We study global-in-time dynamics of the stochastic nonlinear beam equations (SNLB) with an additive space-time white noise, posed on the four-dimensional torus. The roughness of th…
Global well-posedness of one-dimensional cubic fractional nonlinear Schrödinger equations in negative Sobolev spaces
Enguerrand Brun, Guopeng Li, Ruoyuan Liu +1
We study the Cauchy problem for the cubic fractional nonlinear Schrödinger equation (fNLS) on the real line and on the circle. In particular, we prove global well-posedness of the…
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 n…
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}…
Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space
Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov +1
We consider the nonlinear Schrödinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove g…
Local well-posedness of the periodic nonlinear Schrödinger equation with a quadratic nonlinearity in negative Sobolev spaces
Ruoyuan Liu
We study low regularity local well-posedness of the nonlinear Schrödinger equation (NLS) with the quadratic nonlinearity , posed on one-dimensional and two-dimensio…
On the probabilistic well-posedness of the two-dimensional periodic nonlinear Schrödinger equation with the quadratic nonlinearity
Ruoyuan Liu
We study the two-dimensional periodic nonlinear Schrödinger equation (NLS) with the quadratic nonlinearity . In particular, we study the quadratic NLS with random initial da…
Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations
Ruoyuan Liu
We study well-posedness of viscous nonlinear wave equations (vNLW) on the two-dimensional torus with a stochastic forcing. In particular, we prove pathwise global well-posedness of…
Sharp local well-posedness of the two-dimensional periodic nonlinear Schrödinger equation with a quadratic nonlinearity
Ruoyuan Liu, Tadahiro Oh
We study the nonlinear Schrödinger equation (NLS) with the quadratic nonlinearity , posed on the two-dimensional torus . While the relevant -Strichartz es…
On the two-dimensional singular stochastic viscous nonlinear wave equations
Ruoyuan Liu, Tadahiro Oh
We study the stochastic viscous nonlinear wave equations (SvNLW) on , forced by a fractional derivative of the space-time white noise . In particular, we consider S…