18 citations · 23 across the 13 of their papers we have counts for
14 papers
A remark on pathwise well-posedness of the 1- stochastic heat equation
Yufei Shao, Jiawei Li, Tadahiro Oh
We study pathwise well-posedness of the stochastic heat equation (SHE) with a multiplicative noise on the circle. By combining the convolution Young and rough integration theory, i…
Refined global well-posedness for the periodic modulated Korteweg-de Vries equation
Damiano Greco, Massimiliano Gubinelli, Shao Liu +1
We revisit the pathwise global well-posedness issue of the modulated Korteweg-de Vries equation (KdV) on the circle. In the previous work (2024), by combining the -method and th…
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…
Fourier restriction norm method adapted to controlled paths: stochastic wave equations
Andreia Chapouto, Jiawei Li, Tadahiro Oh
We investigate the pathwise well-posedness issue of the stochastic nonlinear wave equation (SNLW) with a multiplicative noise. While the Ito solution theory (= random field solutio…
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…
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…
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…
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…
A simple construction of the sine-Gordon model via stochastic quantization
Massimiliano Gubinelli, Martin Hairer, Tadahiro Oh +1
We present a simple PDE construction of the sine-Gordon measure below the first threshold ($\be^2 < 4π$), in both the finite and infinite volume settings, by studying the correspon…
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…
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 (…
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…