Scattering theory in a weighted L² space for a class of the defocusing inhomogeneous nonlinear Schrödinger equation

2017/10/03 by Dinh, Van Duong · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.01392

Abstract

In this paper, we consider the following inhomogeneous nonlinear Schrödinger equation (INLS) i∂_t u + Δu + μ|x|^-b |u|^αu = 0, (t,x)∈ ℝ × ℝ^d with b, α>0. First, we revisit the local well-posedness in H¹(ℝ^d) for (INLS) of Guzmán [Nonlinear Anal. Real World Appl. 37 (2017), 249-286] and give an improvement of this result in the two and three spatial dimensional cases. Second, we study the decay of global solutions for the defocusing (INLS), i.e. μ=-1 when 0

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• Well-posedness and scattering of odd solutions for the defocusing INLS in one dimension

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