Almost sure well-posedness for the cubic nonlinear Schrödinger equation in the super-critical regime on \TTT^d, d≥ 3

2018/08/02 by Haitian Yue, Yue, Haitian · 2 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1808.00657

openalex publication_date 2018/08/02 · openalex created_date 2018/08/22 · openalex updated_date 2026/07/28

Abstract

In this paper we prove almost sure local well-posedness in both atomic spaces X^s and Fourier restriction spaces X^{s, b} for the cubic nonlinear Schrödinger equation on \TTT^d (d≥ 3) in the super-critical regime.

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• Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two
• Almost sure global well-posedness for the energy supercritical NLS on the unit ball of ℝ³

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