2022/11/06 by Chenjie Fan, Gigliola Staffilani, Fan, Chenjie +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2211.03124
openalex publication_date 2022/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing Nonlinear Schrödinger equation with various initial data, deterministic and random. We show that nonlinear solutions enjoy the same decay rate as the linear ones. The regularity assumption on the initial data is much lower than in previous results (see \citefan2021decay and the references therein) and moreover we quantify the decay, which is another novelty of this work. Furthermore, we show that the (physical) randomization of the initial data can be used to replace the L1-data assumption (see \citefan2022note for the necessity of the L1-data assumption). At last, we note that this method can be also applied to derive decay estimates for other nonlinear dispersive equations.