Minimal blow-up initial data for potential blow-up solutions to inter-critical Schrödinger equations. Issue 6 (26th April 2021) - Guo, Qing; Wang, Hua; Wang, Xuewen
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.