Global Well-Posedness of the Energy-Critical Nonlinear Schrödinger Equation on \mathbbT⁴

2018/05/24 by Haitian Yue, Yue, Haitian · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1805.09816

openalex publication_date 2018/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first prove global well-posedness for the defocusing cubic nonlinear Schrödinger equation (NLS) on 4-dimensional tori - either rational or irrational - and with initial data in H¹. Furthermore, we prove that if a maximal-lifespan solution of the focusing cubic NLS u: I×\mathbbT⁴→ ℂ satisfies sup_{t∈ I}‖u(t)‖_H¹(\mathbbT⁴)

Citations

• Well-posedness and scattering for NLS on \R^d× \T in the energy space
• Bilinear eigenfunction estimates and the nonlinear Schr�dinger equation on surfaces
• On scattering for the cubic defocusing nonlinear Schrödinger equation on waveguide ℝ²× \mathbbT

Cited by

• Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold

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