Blow-up criteria and instability of standing waves for the inhomogeneous fractional Schrodinger equation
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Date
2021-05-07
Authors
Feng, Binhua
He, Zhiqian
Liu, Jiayin
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Inhomogeneous fractional Schrödinger equation, Blow-up criteria, Strong instability
Citation
Feng, B., He, Z., & Liu, J. (2021). Blow-up criteria and instability of standing waves for the inhomogeneous fractional Schrodinger equation. <i>Electronic Journal of Differential Equations, 2021</i>(39), pp. 1-18.