On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations

Abstract

In this paper we study spatial analyticity of solutions to the defocusing nonlinear Schrödinger equations iut + ∆u = |u| p−1 u, given initial data which is analytic with fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time t cannot decay faster than 1/|t| as |t| → ∞. This extends the previous work of Tesfahun [19] for the cubic case p = 3 to the cases where p is any odd integer greater than 3.2010 Mathematics Subject Classification. Primary: 32D15; Secondary: 35Q55.

Improved lower bounds of analytic radius for the Benjamin-Bona-Mahony equation

“…(2) Establish an almost conservation law in G σ,1 , namely 1 This approach is introduced by Selberg and Tesfahun in [10], can be understood a variant I-method [11] in analytic spaces. The method is powerful and has been used to establish analytic radius lower bounds for KdV equations [12,13,14,15,16], KdV-BBM equations [17,18] and other dispersive equations [19,20,21,22,23,24]. For more results on the analytic radius, we refer to the survey [25].…”