20 citations · 32 across the 19 of their papers we have counts for
21 papers
Almost sure global well-posedness for the Benjamin-Bona-Mahony equation
Justin Forlano
We prove that the Benjamin-Bona-Mahony equation is almost surely globally well-posed with respect to random Gaussian initial data of negative Sobolev regularity in $H^{s}(\mathbb{T…
Sub-critical well-posedness for the intermediate nonlinear Schrödinger equation on the line
Andreia Chapouto, Justin Forlano, Thierry Laurens
We continue our study of the well-posedness theory for the intermediate nonlinear Schrödinger equation (INLS). Firstly, we prove that INLS is locally well-posed in $H^s (\mathbb{R}…
Local and global well-posedness for the extended Schrödinger-Benjamin-Ono system
Puti Dai, Justin Forlano
We study the well-posedness problem for the extended Schrödinger-Benjamin-Ono system (eSBO) on the real line. This system couples a Schrödinger field with a Benjamin-Ono type f…
Well-posedness for the periodic Intermediate nonlinear Schrödinger equation
Andreia Chapouto, Justin Forlano, Thierry Laurens
We study the well-posedness for the intermediate nonlinear Schrödinger equation (INLS) with periodic boundary conditions. Using a gauge transform, we obtain large data local well-p…
Invariant Gibbs dynamics for the hyperbolic sinh-Gordon model
Justin Forlano, Younes Zine
We study the hyperbolic defocusing sinh-Gordon model with parameter and its associated Gibbs dynamics on the two-dimensional torus. We establish global well-posedness of th…
On the well-posedness of the intermediate nonlinear Schrödinger equation on the line
Andreia Chapouto, Justin Forlano, Thierry Laurens
We consider a family of intermediate nonlinear Schrödinger equations (INLS) on the real line, which includes the continuum Calogero-Moser models (CCM). We prove that INLS is locall…
Invariant Gibbs dynamics for the nonlinear Schrödinger equations on the disc
Justin Forlano, Yuzhao Wang
We consider the two-dimensional defocusing nonlinear Schrödinger equation (NLS) on the unit disc in the plane with the Gibbs initial data under radial symmetry. By using a type of…
Improved quasi-invariance result for the periodic Benjamin-Ono-BBM equation
Justin Forlano
We extend recent results of Genovese-Luca-Tzvetkov (2022) regarding the quasi-invariance of Gaussian measures under the flow of the periodic Benjamin-Ono-BBM (BO-BBM) equation to t…
Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation
Justin Forlano, Leonardo Tolomeo
We consider the stochastic damped nonlinear wave equation on the two-dimensional torus $\mathb…
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…
Invariant measures for mKdV and KdV in infinite volume
Justin Forlano, Rowan Killip, Monica Visan
We construct dynamics for the defocusing real-valued (Miura) mKdV equation on the real line with initial data distributed according to Gibbs measure. We also prove that Gibbs measu…
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…
A continuum of invariant measures for the periodic KdV and mKdV equations
Andreia Chapouto, Justin Forlano
We consider the real-valued defocusing modified Korteweg-de Vries equation (mKdV) on the circle. Based on the complete integrability of mKdV, Killip-Vişan-Zhang (2018) discovered a…
Quasi-invariance of Gaussian measures of negative regularity for fractional nonlinear Schrödinger equations
Justin Forlano, Leonardo Tolomeo
We consider the Cauchy problem for the fractional nonlinear Schrödinger equation (FNLS) on the one-dimensional torus with cubic nonlinearity and high dispersion parameter , s…
A remark on the well-posedness of the modified KdV equation in
Justin Forlano
We study the real-valued modified KdV equation on the real line and the circle, in both the focusing and the defocusing case. By employing the method of commuting flows introduced…
On the unique ergodicity for a class of 2 dimensional stochastic wave equations
Justin Forlano, Leonardo Tolomeo
We study the global-in-time dynamics for a stochastic semilinear wave equation with cubic defocusing nonlinearity and additive noise, posed on the -dimensional torus. The noise…
Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations
Justin Forlano, Kihoon Seong
We study the transport property of Gaussian measures on Sobolev spaces of periodic functions under the dynamics of the one-dimensional cubic fractional nonlinear Schrödinger equati…
A remark on norm inflation for nonlinear wave equations
Justin Forlano, Mamoru Okamoto
In this note, we study the ill-posedness of nonlinear wave equations (NLW). Namely, we show that NLW experiences norm inflation at every initial data in negative Sobolev spaces. Th…
Almost sure global well posedness for the BBM equation with infinite initial data
Justin Forlano
We consider the probabilistic Cauchy problem for the Benjamin-Bona-Mahony equation (BBM) on the one-dimensional torus with initial data below . With…
On the transport of Gaussian measures under the one-dimensional fractional nonlinear Schrödinger equations
Justin Forlano, William J. Trenberth
Under certain regularity conditions, we establish quasi-invariance of Gaussian measures on periodic functions under the flow of cubic fractional nonlinear Schrödinger equations on…
Stochastic nonlinear Schrödinger equation with almost space-time white noise
Justin Forlano, Tadahiro Oh, Yuzhao Wang
We study the stochastic cubic nonlinear Schrödinger equation (SNLS) with an additive noise on the one-dimensional torus. In particular, we prove local well-posedness of the (renorm…