154 citations · 666 across the 66 of their papers we have counts for
9 papers · 2 filters
On global well-posedness of the modified KdV equation in modulation spaces
Tadahiro Oh, Yuzhao Wang
We study well-posedness of the complex-valued modified KdV equation (mKdV) on the real line. In particular, we prove local well-posedness of mKdV in modulation spaces $M^{2,p}_{s}(…
Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity
Massimiliano Gubinelli, Herbert Koch, Tadahiro Oh
Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonline…
Normal form approach to the one-dimensional periodic cubic nonlinear Schrödinger equation in almost critical Fourier-Lebesgue spaces
Tadahiro Oh, Yuzhao Wang
In this paper, we study the one-dimensional cubic nonlinear Schrödinger equation (NLS) on the circle. In particular, we develop a normal form approach to study NLS in almost critic…
Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces
Tadahiro Oh, Yuzhao Wang
In this paper, we first introduce a new function space whose norm is given by the -sum of modulated -norms of a given function. In particular, when $θ< -\f…
On the probabilistic Cauchy theory for nonlinear dispersive PDEs
Árpád Bényi, Tadahiro Oh, Oana Pocovnicu
In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.
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…