154 citations · 666 across the 66 of their papers we have counts for
6 papers · 2 filters
A remark on normal forms and the "upside-down" I-method for periodic NLS: growth of higher Sobolev norms
James Colliander, Soonsik Kwon, Tadahiro Oh
We study growth of higher Sobolev norms of solutions to the one-dimensional periodic nonlinear Schrodinger equation (NLS). By a combination of the normal form reduction and the ups…
On the one-dimensional cubic nonlinear Schrodinger equation below L^2
Tadahiro Oh, Catherine Sulem
In this paper, we review several recent results concerning well-posedness of the one-dimensional, cubic Nonlinear Schrodinger equation (NLS) on the real line R and on the circle T…
White noise for KdV and mKdV on the circle
Tadahiro Oh
We survey different approaches to study the invariance of the white noise for the periodic KdV. We mainly discuss the following two methods. First, we discuss the PDE method, follo…
Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
Andrea Nahmod, Tadahiro Oh, Luc Rey-Bellet +1
In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrödinger equation in one dimension and establish global well-pose…
Remarks on nonlinear smoothing under randomization for the periodic KdV and the cubic Szegö equation
Tadahiro Oh
We consider Cauchy problems of some dispersive PDEs with random initial data. In particular, we construct local-in-time solutions to the mean-zero periodic KdV almost surely for th…
On unconditional well-posedness of modified KdV
Soonsik Kwon, Tadahiro Oh
Bourgain(1993) proved that the periodic modified KdV equation (mKdV) is locally well-posed in Sobolev spave H^s(T), s >= 1/2, by introducing new weighted Sobolev spaces X^s,b, wher…