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 the inhomogeneous fractional Schrödinger equation i∂tu - (-∆)su + |x|-b|u|pu = 0, where s ∈ (1/2, 1), 0 < b < min{2s, N} and 0 < p < 4s-2b/N-2s. In the L2-critical and L2-supercritical cases, i.e., 4s-2b/N ≤ p < 4s-2b/N-2s, we establish general blow-up criteria for non-radial solutions by using localized viral estimates. Based on these blow-up criteria, we prove the strong instability of standing waves.