On instability of standing waves for the mass-supercritical fractional nonlinear Schrödinger equation

Abstract

We consider the focusing $L^2$-supercritical fractional nonlinear Schrödinger equation \[ i\partial_t u - (-Δ)^s u = -|u|^αu, \quad (t,x) \in \mathbb{R}^+ \times \mathbb{R}^d, \] where $d\ge 2,\frac{d}{2d-1}\le s<1$ and $\frac{4s}{d}<\alpha <\frac{4s}{d-2s}$. By means of the localized virial estimate, we prove that the ground state standing wave is strongly unstable by blow-up. This result is a complement to a recent result of Peng-Shi [J. Math. Phys. 59 (2018), 011508] where the stability and instability of standing waves were studied in the $L^2$-subcritical and $L^2$-critical cases.

14 pages

References in corpus (2)

• On fractional Schrodinger systems of Choquard type
• Existence and stability of standing waves for nonlinear fractional Schrödinger equation with logarithmic nonlinearity