profile decomposition
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Nonlinearity ◽  
2021 ◽  
Vol 34 (7) ◽  
pp. 4787-4818
Author(s):  
José Carlos de Albuquerque ◽  
Diego Ferraz ◽  
Edcarlos D Silva

2020 ◽  
Vol 10 (1) ◽  
pp. 311-330 ◽  
Author(s):  
Feng Binhua ◽  
Ruipeng Chen ◽  
Jiayin Liu

Abstract In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation $$\begin{array}{} \displaystyle i\partial_t\psi- (-{\it\Delta})^s \psi+(I_\alpha \ast |\psi|^{p})|\psi|^{p-2}\psi=0. \end{array}$$ 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.


2019 ◽  
Vol 485 (4) ◽  
pp. 5021-5034 ◽  
Author(s):  
Se-Heon Oh ◽  
Lister Staveley-Smith ◽  
Bi-Qing For

2019 ◽  
Vol 16 (01) ◽  
pp. 73-129 ◽  
Author(s):  
Zehua Zhao

We consider the problem of large data scattering for the defocusing cubic nonlinear Schrödinger equation on [Formula: see text]. This equation is critical both at the level of energy and mass. The key ingredients are global-in-time Stricharz estimate, resonant system approximation, profile decomposition and energy induction method. Assuming the large data scattering for the 2d cubic resonant system, we prove the large data scattering for this problem. This problem is the cubic analogue of a problem studied by Hani and Pausader.


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