Blow-up criteria for fractional nonlinear Schrödinger equation

Abstract

We consider the focusing fractional nonlinear Schrödinger equation \[ i\partial_t u - (-Δ)^s u = -|u|^αu, \quad (t,x) \in \mathbb{R}^+ \times \mathbb{R}^d, \] where $s\in (1/2,1)$ and $\alpha >0$. By using localized virial estimates, we establish general blow-up criteria for non-radial solutions to the equation. As consequences, we obtain blow-up criteria in both $L^2$-critical and $L^2$-supercritical cases which extend the results of Boulenger-Himmelsbach-Lenzmann [{\it Blowup for fractional NLS}, J. Funct. Anal. 271 (2016), 2569--2603] for non-radial initial data.

25 pages. arXiv admin note: text overlap with arXiv:1801.08049

References in corpus (4)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• Numerical study of fractional Nonlinear Schrödinger equations
• Low dimensionality of the diamond surface conductivity
• Sharp Criteria of Scattering for the Fractional NLS