Abstract 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 L2-critical and L2-supercritical cases. Then, we show existence of normalized standing waves by using the profile decomposition theory in Hs. Combining these results, we study the strong instability of normalized standing waves. Our obtained results greatly improve earlier results.

中文翻译：

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分数阶 Schrödinger-Choquard 方程归一化驻波的爆破标准和不稳定性

摘要 在本文中，我们研究了分数阶薛定谔-乔夸德方程 i∂tψ−(−Δ)sψ+(Iα∗|ψ|p)|ψ|p−2ψ=0 的爆破标准和归一化驻波的不稳定性. $$\begin{array}{} \displaystyle i\partial_t\psi- (-{\it\Delta})^s \psi+(I_\alpha \ast |\psi|^{p})|\psi|^ {p-2}\psi=0。\end{array}$$ 通过使用局部维里估计，我们首先在 L2 临界和 L2 超临界情况下为非径向解决方案建立一般的爆炸标准。然后，我们利用 Hs 中的剖面分解理论证明了归一化驻波的存在。结合这些结果，我们研究了归一化驻波的强不稳定性。我们获得的结果大大改善了早期的结果。