18 citations · 41 across the 20 of their papers we have counts for
23 papers
Nonlinear PDEs with modulated dispersion III: multiplicative noises
Andreia Chapouto, Massimiliano Gubinelli, Guopeng Li +2
We investigate pathwise well-posedness of the stochastic modulated Korteweg-de Vries equation (KdV) on the circle with a multiplicative noise, where a time non-homogeneous modulati…
On the singular nature of shallow-water convergence of the intermediate long wave equation on the real line
Andreia Chapouto, Benjamin Harrop-Griffiths, Guopeng Li +1
We investigate regularity properties of the solution map for the intermediate long wave equation (ILW) on the real line. More precisely, we study the scaled ILW which was shown to…
A remark on the log-Sobolev inequality for the Gibbs measure of the focusing Schrödinger equation
Guopeng Li, Jiawei Li, Leonardo Tolomeo
We consider the question of showing a log-Sobolev inequality for the Gibbs measure of the focusing Schrödinger equation built by Lebowitz-Rose-Speer (1988), formally given by $$ dρ…
Shallow-water convergence of the intermediate long wave equation in
Andreia Chapouto, Guopeng Li, Tadahiro Oh +1
We continue our study on the convergence issue of the intermediate long wave equation (ILW) on both the real line and the circle. In particular, we establish convergence of the sca…
Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation
Guopeng Li, Jiawei Li, Tadahiro Oh +1
We investigate a possible extension of probabilistic well-posedness theory of nonlinear dispersive PDEs with random initial data beyond variance blowup. As a model equation, we stu…
Nonlinear PDEs with modulated dispersion IV: normal form approach and unconditional uniqueness
Massimiliano Gubinelli, Guopeng Li, Jiawei Li +1
We study the modulated Korteweg-de~Vries equation (KdV) on the circle with a time non-homogeneous modulation acting on the linear dispersion term. By adapting the normal form appro…
Deep-water and shallow-water limits of statistical equilibria for the intermediate long wave equation
Andreia Chapouto, Guopeng Li, Tadahiro Oh
We study the construction of invariant measures associated with higher order conservation laws of the intermediate long wave equation (ILW) and their convergence properties in the…
Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus
Guopeng Li, Mamoru Okamoto, Liying Tao
We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schrödinger equation (SNLS) on the three dimensional torus, forced by an additive noise. We adapt…
Compact bilinear operators and paraproducts revisited
Árpád Bényi, Guopeng Li, Tadahiro Oh +1
We present a new proof of the compactness of bilinear paraproducts with CMO symbols. By drawing an analogy to compact linear operators, we first explore further properties of compa…
Compact theorem à la Stein
Árpád Bényi, Guopeng Li, Tadahiro Oh +1
We prove a compact theorem, involving quantitative estimates, analogous to the quantitative classical theorem due to Stein. We also discuss the -to-…
Unconditional deep-water limit of the intermediate long wave equation in low-regularity
Justin Forlano, Guopeng Li, Tengfei Zhao
In this paper, we establish the unconditional deep-water limit of the intermediate long wave equation (ILW) to the Benjamin-Ono equation (BO) in low-regularity Sobolev spaces on bo…
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…
Intermediate long wave equation in negative Sobolev spaces
Andreia Chapouto, Justin Forlano, Guopeng Li +2
We study the intermediate long wave equation (ILW) in negative Sobolev spaces. In particular, despite the lack of scaling invariance, we identify the regularity as…
Deep-water limit of the intermediate long wave equation in
Andreia Chapouto, Guopeng Li, Tadahiro Oh +1
We study the well-posedness issue of the intermediate long wave equation (ILW) on both the real line and the circle. By applying the gauge transform for the Benjamin-Ono equation (…
Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation
Guopeng Li, Liying Tao, Tengfei Zhao
We consider the Cauchy problem for the stochastic Hartree nonlinear wave equations (SHNLW) with a cubic convolution nonlinearity and an additive stochastic forcing on the Euclidean…
Optimal divergence rate of the focusing Gibbs measures
Damiano Greco, Guopeng Li, Rui Liang +2
We study Gibbs measures on the -dimensional torus with -(super)critical focusing interaction potentials. We establish a precise divergence rate of the partition function as…
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}…
On the deep-water and shallow-water limits of the intermediate long wave equation from a statistical viewpoint
Guopeng Li, Tadahiro Oh, Guangqu Zheng
(Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here. See the abstract in the paper.) We study convergence proble…
Deep-water and shallow-water limits of the intermediate long wave equation
Guopeng Li
In this paper, we study the low regularity convergence problem for the intermediate long wave equation (ILW), with respect to the depth parameter , on the real line and the ci…
Almost conservation laws for stochastic nonlinear Schrödinger equations
Kelvin Cheung, Guopeng Li, Tadahiro Oh
In this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the -method (= the method of almost conservation law…
Global well-posedness of the 4-d energy-critical stochastic nonlinear Schrödinger equations with non-vanishing boundary condition
Kelvin Cheung, Guopeng Li
We consider the energy-critical stochastic cubic nonlinear Schrödinger equation on with additive noise, and with the non-vanishing boundary conditions at spatial infi…
Nonlinear PDEs with modulated dispersion II: Korteweg-de Vries equation
Khalil Chouk, Massimiliano Gubinelli, Guopeng Li +2
(Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here. See the abstract in the paper.) We study dispersive equatio…