Global well-posedness of the energy-critical defocusing NLS on $\mathbb{R}\times {\mathbb{T}}^3$

Abstract

In this paper we prove global well-posedness in $H^1$ for the energy-critical defocusing initial-value problem \begin{equation*} (i\partial_t+Δ_x)u=u|u|^2,\qquad u(0)=ϕ, \end{equation*} in the semiperiodic setting $x\in\R\times\T^3$.

51 pages; v2: introduction reworked and references added

References in corpus (2)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Global well-posedness of the energy critical Nonlinear Schrödinger equation with small initial data in H^1(T^3)

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• Global well-posedness of the cubic nonlinear Schrödinger equation on compact manifolds without boundary
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• Global Well-Posedness of the Energy-Critical Nonlinear Schrödinger Equation on ${\mathbb{T}}^4$
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• Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ${\mathbb{R}}^2$ $\times$ ${\mathbb{T}}^2$
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• On the decay property of the cubic fourth-order Schrödinger equation
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• Global well-posedness of the cubic nonlinear Schrödinger equation on ${\mathbb{T}}^2$
• On scattering for the cubic defocusing nonlinear Schrödinger equation on waveguide ${\mathbb{R}}^2\times \mathbb{T}$
• Hyperbolic nonlinear Schrödinger equations on $\mathbb{R}\times \mathbb{T}$
• Global endpoint Strichartz estimates for Schrödinger equations on the cylinder $\mathbb{R}\times \mathbb{T}$