Minimal-mass blow-up solutions for inhomogeneous nonlinear Schrödinger equations with growth potentials

2021/08/13 by Matsui, Naoki
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.06205

Abstract

In this paper, we consider the following equation: i(∂ u)/(∂ t)+Δu+g(x)|u|^(4)/(N)u-Wu=0. We construct a critical-mass solution that blows up at a finite time and describe the behaviour of the solution in the neighbourhood of the blow-up time. Banica-Carles-Duyckaertz (2011) has shown the existence of a critical-mass blow-up solution under the assumptions that N≤ 2, that g and W are sufficiently smooth and that each derivative of these is bounded. In this paper, we show the existence of a critical-mass blow-up solution under weaker assumptions regarding smoothness and boundedness of g and W. In particular, it includes the cases where W is growth at spatial infinity or not Lipschitz continuous.

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