Global well-posedness and scattering for the defocusing $H^{\frac{1}{2}}$-subcritical Hartree equation in $R^d$

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1. [1] Cazenave T., Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, vol. 10, New York University Courant Institute of Mathematical Sciences, New York, 2003. Zbl1055.35003MR2002047
2. [2] J. Colliander, M. Grillakis, N. Tzirakis, Improved interaction Morawetz inequalities for the cubic nonlinear Schrödinger equation on $R^2$, IMRN 23 (2007), Art. ID rnm090, 30 pp. Zbl1142.35085MR2377216
3. [3] Colliander J., Keel M., Staffilani G., Takaoka H., Tao T., Global existence and scattering for rough solutions to a nonlinear Schrödinger equations on $R^3$, Comm. Pure Appl. Math.57 (8) (2004) 987-1014. Zbl1060.35131MR2053757
4. [4] Colliander J., Keel M., Staffilani G., Takaoka H., Tao T., Resonant decompositions and the I-method for cubic nonlinear Schrödinger on $R^2$, Discrete Contin. Dynam. Systems21 (3) (2008) 665-686. Zbl1147.35095MR2399431
5. [5] Chae M., Hong S., Kim J., Yang C.W., Scattering theory below energy for a class of Hartree type equations, Comm. Partial Differential Equations33 (2008) 321-348. Zbl1185.35249MR2398232
6. [6] De Silva D., Pavlovic N., Staffilani G., Tzirakis N., Global well-posedness and polynomial bounds for the defocusing $L^2$-critical nonlinear Schrödinger equation in $R$, Comm. Partial Differential Equations33 (2008) 1395-1429. Zbl1155.35310MR2450163
7. [7] Ginibre J., Ozawa T., Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension $n\ge 2$, Comm. Math. Phys.151 (1993) 619-645. Zbl0776.35070MR1207269
8. [8] Ginibre J., Velo G., Scattering theory in the energy space for a class of Hartree equations, in: Nonlinear Wave Equations, Providence, RI, 1998, Contemp. Math., vol. 263, Amer. Math. Soc., Providence, RI, 2000, pp. 29-60. Zbl0966.35095MR1777634
9. [9] Ginibre J., Velo G., Long range scattering and modified wave operators for some Hartree type equations, Rev. Math. Phys.12 (3) (2000) 361-429. Zbl1044.35041MR1755906
10. [10] Ginibre J., Velo G., Long range scattering and modified wave operators for some Hartree type equations II, Ann. Inst. H. Poincaré1 (4) (2000) 753-800. Zbl1024.35084MR1785187
11. [11] Ginibre J., Velo G., Long range scattering and modified wave operators for some Hartree type equations. III: Gevrey spaces and low dimensions, J. Differential Equations175 (2) (2001) 415-501. Zbl0991.35057MR1855975
12. [12] A. Grünrock, New applications of the Fourier restriction norm method to wellposedness problems for nonlinear evolution equations, Dissertation Univ. Wuppertal, 2002. 
13. [13] Hayashi N., Tsutsumi Y., Scattering theory for the Hartree equations, Ann. Inst. H. Poincaré Phys. Théor.61 (1987) 187-213. Zbl0634.35059MR887147
14. [14] Keel M., Tao T., Endpoint Strichartz estimates, Amer. J. Math.120 (5) (1998) 955-980. Zbl0922.35028MR1646048
15. [15] Li D., Miao C., Zhang X., The focusing energy-critical Hartree equation, J. Differential Equations246 (3) (2009) 1139-1163. Zbl1155.35421MR2474589
16. [16] Lin J.E., Strauss W.A., Decay and scattering of solutions of a nonlinear Schrödinger equation, J. Funct. Anal.30 (2) (1978) 245-263. Zbl0395.35070MR515228
17. [17] Miao C., $H^m$-modified wave operator for nonlinear Hartree equation in the space dimensions $n\ge 2$, Acta Math. Sinica13 (2) (1997) 247-268. Zbl0877.35089MR1481805
18. [18] Miao C., Xu G., Zhao L., The Cauchy problem of the Hartree equation. Dedicated to Professor Li Daqian on the occasion of seventieth birthday, J. Partial Differential Equations21 (2008) 22-44. Zbl1174.35099MR2394047
19. [19] Miao C., Xu G., Zhao L., Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data, J. Funct. Anal.253 (2007) 605-627. Zbl1136.35092MR2370092
20. [20] Miao C., Xu G., Zhao L., Global well-posedness and scattering for the energy-critical, defocusing Hartree equation in $R^{1+n}$, arXiv:0707.3254. Zbl1252.35235
21. [21] Miao C., Xu G., Zhao L., Global well-posedness and scattering for the mass-critical Hartree equation with radial data, J. Math. Pures Appl.91 (2009) 49-79. Zbl1154.35078MR2487900
22. [22] Nakanishi K., Energy scattering for Hartree equations, Math. Res. Lett.6 (1999) 107-118. Zbl0949.35104MR1682697
23. [23] Nawa H., Ozawa T., Nonlinear scattering with nonlocal interactions, Comm. Math. Phys.146 (1992) 259-275. Zbl0748.35046MR1165183
24. [24] Tao T., Multilinear weighted convolution of $L^2$ functions, and applications to non-linear dispersive equations, Amer. J. Math.123 (2001) 839-908. Zbl0998.42005MR1854113
25. [25] Tao T., Nonlinear Dispersive Equations. Local and Global Analysis, CBMS Regional Conf. Ser. in Math., vol. 106, Amer. Math. Soc., 2006. Zbl1106.35001MR2233925
26. [26] http://tosio.math.toronto.edu/wiki/index.php/Main_Page.