H^s_x× H^s_x scattering theory for a weighted gradient system of 3D radial defocusing NLS

2021/05/24 by Xianfa Song, Song, Xianfa
Mathematics · Physics and Astronomy · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2105.11579

openalex publication_date 2021/05/24 · openalex created_date 2021/06/07 · openalex updated_date 2026/07/28

Abstract

In this paper, using I-method, we establish H^s_x× H^s_x scattering theories for the following Cauchy problem \ iu_t+Δu=λ|v|²u, iv_t+Δv=μ|u|²v, x∈ ℝ³, t · gt;0,
u(x,0)=u₀(x), v(x,0)=v₀(x), x∈ ℝ³.. Here λ>0, μ>0, (u₀,v₀)∈ H^s_x(ℝ³)× H^s_x(ℝ³) and (1)/(2)

Citations

• Solitons and Scattering for the Cubic–Quintic Nonlinear Schrödinger Equation on ℝ³ R 3
• Global well-posedness and scattering for nonlinear Schr "odinger\n equations with algebraic nonlinearity when d = 2, 3, u₀ radial
• Large global solutions for nonlinear Schrödinger equations III, energy-supercritical cases

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