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

Advances in Nonlinear Analysis

article

Feng Binhua¹  Ruipeng Chen²  Jiayin Liu² 

[1] Department of Mathematics, Northwest Normal University;School of Mathematics and Information Science, North Minzu University

关键词: Fractional Schrödinger-Choquard equation;    Blow-up criteria;    Strong instability;    Normalized standing waves;   

DOI  :  10.1515/anona-2020-0127

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation i∂ tψ − (− Δ )sψ +(Iα ∗ |ψ |p)|ψ |p− 2ψ =0. $$\begin{array}{} \displaystyle i\partial_t\psi- (-{\it\Delta})^s \psi+(I_\alpha \ast |\psi|^{p})|\psi|^{p-2}\psi=0. \end{array}$$ By using localized virial estimates, we firstly establish general blow-up criteria for non-radial solutions in both L 2 -critical and L 2 -supercritical cases. Then, we show existence of normalized standing waves by using the profile decomposition theory in H s . Combining these results, we study the strong instability of normalized standing waves. Our obtained results greatly improve earlier results.

【 授权许可】

CC BY