We consider the mass concentration phenomenon for the L 2 -critical nonlinear Schrödinger equations of higher orders. We show that any solution u to iu t + (−∆) α 2 u = ±|u| 2α d u, u(0, ·) ∈ L 2 for α > 2, which blows up in a finite time, satisfies a mass concentration phenomenon near the blow-up time. We verify that as α increases, the size of region capturing a mass concentration gets wider due to the stronger dispersive effect. 8 d u in (1.1) was studied in [6,12]. When α = 2, it is unknown whether there exists a blow up 2000Mathematics Subject Classification. 35B05, 35B30, 35B33, 35Q55, 42B10 .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.