Blow-up criteria for linearly damped nonlinear Schrödinger equations

2019/12/18 by Dinh, Van Duong
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.08752

Abstract

We consider the Cauchy problem for linearly damped nonlinear Schrödinger equations i∂_t u + Δu + i a u= ± |u|^αu, (t,x) ∈ [0,∞) × ℝ^N, where a>0 and α>0. We prove the global existence and scattering for a sufficiently large damping parameter in the energy-critical case. We also prove the existence of finite time blow-up H¹ solutions to the focusing problem in the mass-critical and mass-supercritical cases.

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