Global well-posedness and scattering for the defocusing ${\dot{H}}^{\frac{1}{2}}$-critical nonlinear Schrödinger equation in ${\mathbb{R}}^2$

Abstract

In this paper we consider the Cauchy initial value problem for the defocusing quintic nonlinear Schrödinger equation in ${\mathbb{R}}^2$ with general data in the critical space ${\dot{H}}^{\frac{1}{2}}({\mathbb{R}}^2)$. We show that if a solution remains bounded in ${\dot{H}}^{\frac{1}{2}}({\mathbb{R}}^2)$ in its maximal interval of existence, then the interval is infinite and the solution scatters.

References in corpus (3)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• The radial defocusing energy-supercritical NLS in dimension four
• A counterexample to an endpoint bilinear Strichartz inequality

Cited by in corpus (1)

• On the global well-posedness for the periodic quintic nonlinear Schrödinger equation