6 papers
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…
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…
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…