154 citations · 666 across the 66 of their papers we have counts for
11 papers · 1 filter
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…
Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions
Trishen S. Gunaratnam, Tadahiro Oh, Nikolay Tzvetkov +1
We prove quasi-invariance of Gaussian measures supported on Sobolev spaces under the dynamics of the three-dimensional defocusing cubic nonlinear wave equation. As in the previous…
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…
Modulation spaces with scaling symmetry
Árpád Bényi, Tadahiro Oh
We indicate how to construct a family of modulation function spaces that have a scaling symmetry. We also illustrate the behavior of the Schrödinger multiplier on such function spa…