Local well-posedness for cubic fractional Schrödinger equations with derivatives on the right-hand side

2025/03/26 by Ahmed Dughayshim, Dughayshim, Ahmed, Silvino Reyes Farina +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2503.20971

openalex publication_date 2025/03/26 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

For s ∈ ((1)/(2),1] we investigate well-posedness of the equation ( i ∂_t + (-Δ)^s ) u = (|D|^1-2s |u|² ) |D|^2s-1 u under small initial data ‖u(0)‖_{H^(n-2s)/(2)(ℝⁿ)} ≪ 1. This equation is a model equation for for s-Schrödinger map equation ∂_t ψ= ψ\wedge (-Δ)^s ψ: ψ: ℝⁿ × ℝ → \mathbbS²,

Related

• Almost Sure Global Well-posedness for Fractional Cubic Schr "odinger\n equation on torus
• Well-posedness and Ill-posedness for the cubic fractional Schrödinger equations
• Global Well-posedness for the periodic fractional cubic NLS in 1D
• Global well-posedness of cubic fractional Schrödinger equations in one dimension
• L² solutions for cubic NLS equation with fractional elliptic/hyperbolic operators on ℝ×\mathbbT and ℝ²