Blow-up criteria and instability of standing waves for the inhomogeneous fractional Schrodinger equation

Abstract

In this article, we study the blow-up and instability of standing waves for theinhomogeneous fractional Schrodinger equation $$ i\partial_tu-(-\Delta)^su+ |x|^{-b}|u|^{p}u=0, $$ where \(s\in (\frac{1}{2},1)\), \(0<b<\min \{2s,N\}\) and \(0<p< \frac{4s-2b}{N-2s}\). In the \(L^2\)-critical and \(L^2\)-supercritical cases, i.e.,\(\frac{4s-2b}{N}\leq p< \frac{4s-2b}{N-2s}\), we establish general blow-up criteriafor non-radial solutions by using localized virial estimates. Based on theseblow-up criteria, we prove the strong instability of standing waves.
 For more information see https://ejde.math.txstate.edu/Volumes/2021/39/abstr.html