Answers are grounded in this paper and cite their sources.
This work demonstrates local well-posedness of cubic fractional Schrödinger equations, highlighting the role of small initial data.
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)\|_Hn-2s/2(Rⁿ) 1. This equation is a model equation for for s-Schr\"odinger map equation \[ ∂_t ψ = ψ (-Δ)^s ψ: ψ: R^n × R → S², \]
No takes yet. Share an insight, caveat, or question.
Dughayshim et al. (2025) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: