References
- Lewin M, Rougerie N. Derivation of Pekar´s polarons from a microscopic model of quantum crystal. SIAM J Math Anal. 2013;45:1267–1301. doi: https://doi.org/10.1137/110846312
- Lions P-L. The Choquard equation and related questions. Nonlinear Anal. 1980;4:1063–1072. doi: https://doi.org/10.1016/0362-546X(80)90016-4
- Gross EP, Meeron E. Physics of many-particle systems. Gordon Breach New York. 1966;1:231–406.
- Elgart A, Schlein B. Mean field dynamics of boson stars. Commun Pure Appl Math. 2007;60:500–545. doi: https://doi.org/10.1002/cpa.20134
- Lenzmann E. Well-posedness for semi-relativistic Hartree equations of critical type. Math Phys Anal Geom. 2007;10:43–64. doi: https://doi.org/10.1007/s11040-007-9020-9
- Fröhlich J, Lenzmann E. Mean-field limit of quantum Bose gases and nonlinear Hartree equation. Sémin. Équ. Dériv. Partielles, Ecole Polytechique, Palaiseau, Exp. No. XIX, p.26(2003-2004).
- Spohn H. On the Vlasov hierarchy. Math Method Appl Sci. 1981;3:445–455. doi: https://doi.org/10.1002/mma.1670030131
- Feng B, Yuan X. On the Cauchy problem for the Schrödinger-Hartree equation. Evol Equat Cont Theory. 2015;4(4):431–445. doi: https://doi.org/10.3934/eect.2015.4.431
- Saanouni T. Scattering threshold for the focusing Choquard equation. Nonlinear Differ Equ Appl. 2019;26(41).
- Bonanno C, d'Avenia P, Ghimenti M, et al. Soliton dynamics for the generalized Choquard equation. J Math Anal Appl. 2014;417:180–199. doi: https://doi.org/10.1016/j.jmaa.2014.02.063
- Chen J, Guo B. Strong instability of standing waves for a nonlocal Schrödinger equation. Physica D. 2007;227:142–148. doi: https://doi.org/10.1016/j.physd.2007.01.004
- Genev H, Venkov G. Soliton and blow-up solutions to the time-dependent Schrödinger Hartree equation. Discrete Contin Dyn Syst Ser S. 2012;5:903–923.
- Moroz V, Schaftingen JV. Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics. J Funct Anal. 2013;265:153–184. doi: https://doi.org/10.1016/j.jfa.2013.04.007
- Saanouni T. A note on the fractional Schrödinger equation of Choquard type. J Math Anal Appl. 2019;470:1004–1029. doi: https://doi.org/10.1016/j.jmaa.2018.10.045
- Saanouni T. Sharp threshold of global well-posedness vs finite time blow-up for a class of inhomogeneous Choquard equations. J Math Phys. 2019;60:081514.
- Boulenger T, Himmelsbach D, Lenzmann E. Blow-up for fractional NLS. J Funct Anal. 2016;271:2569–2603. doi: https://doi.org/10.1016/j.jfa.2016.08.011
- Adams R. Sobolev spaces. New York: Academic; 1975.
- Cho Y, Ozawa T. Sobolev inequalities with symmetry. Commun Contemp Math. 2009;11(3):355–365. doi: https://doi.org/10.1142/S0219199709003399
- Lions P-L. Symétrie et compacité dans les espaces de Sobolev. J Funct Anal. 1982;49(3):315–334. doi: https://doi.org/10.1016/0022-1236(82)90072-6
- Christ M, Weinstein M. Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation. J Funct Anal. 1991;100:87–109. doi: https://doi.org/10.1016/0022-1236(91)90103-C
- Lieb E. Analysis. 2nd ed. Vol 14. Providence (RI): American Mathematical Society; 2001. (Graduate Studies in Mathematics).
- Le Coz S. A note on Berestycki-Cazenave classical instability result for nonlinear Schrödinger equations. Adv Nonlinear Stud. 2008;8(3):455–463. doi: https://doi.org/10.1515/ans-2008-0302
- Shirai Shin-ichi. Some applications of the Pohozaev identity. J Math Phys. 2009;50:042108. doi: https://doi.org/10.1063/1.3115044
- Guo Z, Wang Y. Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations. J Anal Math. 2014;124(1):1–38. doi: https://doi.org/10.1007/s11854-014-0025-6