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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…