Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations

2020/01/08 by Dinh, Van Duong · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.03022

Abstract

We consider the following class of focusing L²-supercritical fourth-order nonlinear Schrödinger equations i∂_t u - Δ² u + μΔu = - |u|^αu, (t,x) ∈ ℝ × ℝ^N, where N≥ 2, μ≥ 0, and (8)/(N) 0, our blow-up result extends an earlier result proved by Boulenger-Lenzmann \citeBL, where the finite time blow-up was shown for initial data with negative energy.

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