On the low-regularity global well-posedness of a system of nonlinear Schrodinger Equation

2017/04/17 by Chenmin Sun, Sun, Chenmin
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1704.05013

openalex publication_date 2017/04/17 · openalex created_date 2017/04/28 · openalex updated_date 2026/07/28

Abstract

In this article, we study the low-regularity Cauchy problem of a one dimensional quadratic Schrodinger system with coupled parameter α∈ (0, 1). When (1)/(2)<α<1,we prove the global well-posedness in H^s(ℝ) with s>-(1)/(4), while for 0<α<(1)/(2), we obtain global well-posedness in H^s(ℝ) with s>-(5)/(8). We have adapted the linear-nonlinear decomposition and resonance decomposition technique in different range of α.

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