On Fractional Schrodinger Equations in sobolev spaces

2015/01/07 by Hong, Younghun, Sire, Yannick · 4 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.01414

Abstract

Let σ∈(0,1) with σ≠(1)/(2). We investigate the fractional nonlinear Schrödinger equation in \mathbb R^d: i∂_tu+(-Δ)^σu+μ|u|^p-1u=0, u(0)=u₀∈ H^s, where (-Δ)^σ is the Fourier multiplier of symbol |ξ|^2σ, and μ=± 1. This model has been introduced by Laskin in quantum physics \citelaskin. We establish local well-posedness and ill-posedness in Sobolev spaces for power-type nonlinearities.

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