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

Abstract

In this paper, we consider the initial value problem for the quintic, defocusing nonlinear Schrödinger equation on ${\mathbb{T}}^2$ with general data in the critical Sobolev space $H^{\frac{1}{2}}({\mathbb{T}}^2)$. We show that if a solution remains bounded in $H^{\frac{1}{2}}({\mathbb{T}}^2)$ in its maximal interval of existence, then the solution is globally well-posed in ${\mathbb{T}}^2$.

References in corpus (4)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Global Well-posedness for the focusing cubic NLS on the product space $\mathbb{R}\times {\mathbb{T}}^3$
• Multilinear Eigenfunction Estimates And Global Existence For The Three Dimensional Nonlinear SchrÖdinger Equations
• Global Well-posedness of the Energy-Critical Defocusing NLS on Rectangular Tori in three Dimensions