Mass concentration for the L²-critical Nonlinear Schrödinger equations of higher orders

2009/04/20 by Chae, Myeongju, Hong, Sunggeum, Lee, Sanghyuk
#35B05 #35B30 #35B33 #35Q55 #42B10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0904.3021

Abstract

We consider the mass concentration phenomenon for the L²-critical nonlinear Schrödinger equations of higher orders. We show that any solution u to iu_t + (-Δ)^\fracα2 u =± |u|^(2α)/(d)u, u(0,⋅)∈ L² 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.

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