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We prove global well-posedness for low regularity data for the L 2 − critical defocusing nonlinear Schrödinger equation (NLS) in 2d. More precisely we show that a global solution exists for initial… (More)

We prove low regularity global well-posedness for the 1d Zakharov system and the 3d Klein-Gordon-Schrödinger system, which are systems in two variables u : Rx × Rt → C and n : Rx × Rt → R. The… (More)

The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for H initial data, s > −1/2, and for any s1 < min(3s+1, s+ 1), the difference of the nonlinear… (More)

In this paper we study the local and global regularity properties of the cubic nonlinear Schrödinger equation (NLS) on the half line with rough initial data. These properties include local and global… (More)

The initial value problem for the L critical semilinear Schrödinger equation with periodic boundary data is considered. We show that the problem is globally well posed in H(T), for s > 4/9 and s >… (More)

We study the evolution of the one dimensional periodic cubic Schrödinger equation (NLS) with bounded variation data. For the linear evolution, it is known that for irrational times the solution is a… (More)

This article consists of two parts. In the first part, we review the most recent proofs establishing quadratic Morawetz inequalities for the nonlinear Schrödinger equation (NLS). We also describe the… (More)

The forced and weakly damped Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. Starting from L and mean-zero initial data we prove that the solution decomposes into… (More)