The Cauchy problem for the energy-critical inhomogeneous nonlinear Schrödinger equation with inverse-square potential

2021/07/21 by Jang, RoeSong, An, JinMyong, Kim, JinMyong
#35A01 #35B44 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.09826

Abstract

In this paper, we study the Cauchy problem for the energy-critical inhomogeneous nonlinear Schrödinger equation with inverse-square potential iu_t +Δu-c|x|^-2u=λ|x|^-b |u|^σ u, u(0)=u₀ ∈ H¹, (t,x)∈ \mathbb R×\mathbb R^d, where d≥3, λ=±1, 0<b>-c(d):=-((d-2)/(2))². We first prove the local well-posedness as well as small data global well-posedness and scattering in H¹ for c&gt;-\frac(d+2-2b)²-4(d+2-2b)²c(d) and 0<b></b></b>

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