Minimal blow-up initial data for potential blow-up solutions to inter-critical Schrödinger equations. Issue 6 (26th April 2021)

• Record Type: Journal Article
• Authors: Guo, Qing; Wang, Hua; Wang, Xuewen
• Is Part Of: Applicable analysis. Volume 100:Issue 6(2021)
• Page Start: 1213
• Page End: 1228
• Publication Date: 2021-04-26
• Subjects: Nonlinear Schrödinger equation -- inter-critical -- blow-up -- profile decomposition; 35Q55; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1636972
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We show that assuming some initial datum u 0 ∈ a ˙ H s c ( R d ) leads to a blow-up solution of the inter-critical defocusing nonlinear Schrödinger equation, there must exist an initial datum with the minimal H ˙ s c -norm which will produce blow-up. Moreover, up to the invariant transformations, the set of such data is compact in H ˙ s c ( R d ) . The main tool is the profile decomposition combined with the perturbation argument.