Blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation

In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation By using localized virial estimates, we firstly establish general blow-up criteria for non-radial solutions in both -critical and -supercritical cases. Then, we show existence of normalized standing waves by using the profile decomposition theory in . Combining these results, we study the strong instability of normalized standing waves. Our obtained results greatly improve earlier results.