An Improvement on the Brézis-Gallouët technique for 2D NLS and 1D half-wave equation

Abstract

We revise the classical approach by Brézis-Gallouët to prove global well posedness for nonlinear evolution equations. In particular we prove global well--posedness for the quartic NLS posed on general domains $\Omega$ in ${\mathbb{R}}^2$ with initial data in $H^2(\Omega )\cap H_0^1(\Omega )$, and for the quartic nonlinear half-wave equation on $\mathbb{R}$ with initial data in $H^1(\mathbb{R})$.

References in corpus (1)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation