pseudoconformal

Specifically, we (1) obtain a sharp Gagliardo-Nirenberg inequality analogous to Weinstein (1983), (2) apply the sharp Gagliardo-Nirenberg inequality and a local virial identity to obtain a sharp global existence/blow-up threshold analogous to Weinstein (1983), Glassey (1977) in the case #92;sigma#95;c#61;0 and Duyckaerts, Holmer, & Roudenko (2008), Guevara (2014), and Fang, Xie, & Cazenave (2011) for 0lt;#92;sigma#95;clt;1, (3) prove a sharp mass concentration result in the L² critical case analogous to Tsutsumi (1990), Merle & Tsutsumi (1990) and (4) show that minimal mass blow-up solutions in the L² critical case are pseudoconformal transformations of the ground state, analogous to Merle (1993)..

2015, Justin Holmer, Chang Liu, “Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity I: Basic theory”, in arXiv