@article{AIHPC_2009__26_5_1831_0, author = {Miao, Changxing and Xu, Guixiang and Zhao, Lifeng}, title = {Global {Well-Posedness} and {Scattering} for the {Defocusing} ${H}^{\frac{1}{2}}${-Subcritical} {Hartree} {Equation} in ${R}^{d}$}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1831--1852}, publisher = {Elsevier}, volume = {26}, number = {5}, year = {2009}, doi = {10.1016/j.anihpc.2009.01.003}, mrnumber = {2566712}, zbl = {1176.35140}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.003/} }
TY - JOUR AU - Miao, Changxing AU - Xu, Guixiang AU - Zhao, Lifeng TI - Global Well-Posedness and Scattering for the Defocusing ${H}^{\frac{1}{2}}$-Subcritical Hartree Equation in ${R}^{d}$ JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 1831 EP - 1852 VL - 26 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.003/ DO - 10.1016/j.anihpc.2009.01.003 LA - en ID - AIHPC_2009__26_5_1831_0 ER -
%0 Journal Article %A Miao, Changxing %A Xu, Guixiang %A Zhao, Lifeng %T Global Well-Posedness and Scattering for the Defocusing ${H}^{\frac{1}{2}}$-Subcritical Hartree Equation in ${R}^{d}$ %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 1831-1852 %V 26 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.003/ %R 10.1016/j.anihpc.2009.01.003 %G en %F AIHPC_2009__26_5_1831_0
Miao, Changxing; Xu, Guixiang; Zhao, Lifeng. Global Well-Posedness and Scattering for the Defocusing ${H}^{\frac{1}{2}}$-Subcritical Hartree Equation in ${R}^{d}$. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1831-1852. doi : 10.1016/j.anihpc.2009.01.003. http://www.numdam.org/articles/10.1016/j.anihpc.2009.01.003/
[1] Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, vol. 10, New York University Courant Institute of Mathematical Sciences, New York, 2003. | MR | Zbl
,[2] J. Colliander, M. Grillakis, N. Tzirakis, Improved interaction Morawetz inequalities for the cubic nonlinear Schrödinger equation on , IMRN 23 (2007), Art. ID rnm090, 30 pp. | MR | Zbl
[3] Global Existence and Scattering for Rough Solutions to a Nonlinear Schrödinger Equations on , Comm. Pure Appl. Math. 57 (8) (2004) 987-1014. | MR | Zbl
, , , , ,[4] Resonant Decompositions and the I-Method for Cubic Nonlinear Schrödinger on , Discrete Contin. Dynam. Systems 21 (3) (2008) 665-686. | MR | Zbl
, , , , ,[5] Scattering Theory Below Energy for a Class of Hartree Type Equations, Comm. Partial Differential Equations 33 (2008) 321-348. | MR
, , , ,[6] Global Well-Posedness and Polynomial Bounds for the Defocusing -Critical Nonlinear Schrödinger Equation in , Comm. Partial Differential Equations 33 (2008) 1395-1429. | MR | Zbl
, , , ,[7] Long Range Scattering for Nonlinear Schrödinger and Hartree Equations in Space Dimension , Comm. Math. Phys. 151 (1993) 619-645. | MR | Zbl
, ,[8] 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. | MR | Zbl
, ,[9] Long Range Scattering and Modified Wave Operators for Some Hartree Type Equations, Rev. Math. Phys. 12 (3) (2000) 361-429. | MR | Zbl
, ,[10] Long Range Scattering and Modified Wave Operators for Some Hartree Type Equations II, Ann. Inst. H. Poincaré 1 (4) (2000) 753-800. | MR | Zbl
, ,[11] Long Range Scattering and Modified Wave Operators for Some Hartree Type Equations. III: Gevrey Spaces and Low Dimensions, J. Differential Equations 175 (2) (2001) 415-501. | MR | Zbl
, ,[12] A. Grünrock, New applications of the Fourier restriction norm method to wellposedness problems for nonlinear evolution equations, Dissertation Univ. Wuppertal, 2002.
[13] Scattering Theory for the Hartree Equations, Ann. Inst. H. Poincaré Phys. Théor. 61 (1987) 187-213. | Numdam | MR | Zbl
, ,[14] Endpoint Strichartz Estimates, Amer. J. Math. 120 (5) (1998) 955-980. | MR | Zbl
, ,[15] The Focusing Energy-Critical Hartree Equation, J. Differential Equations 246 (3) (2009) 1139-1163. | MR | Zbl
, , ,[16] Decay and Scattering of Solutions of a Nonlinear Schrödinger Equation, J. Funct. Anal. 30 (2) (1978) 245-263. | MR | Zbl
, ,[17] -Modified Wave Operator for Nonlinear Hartree Equation in the Space Dimensions , Acta Math. Sinica 13 (2) (1997) 247-268. | MR | Zbl
,[18] The Cauchy Problem of the Hartree Equation. Dedicated to Professor Li Daqian on the Occasion of Seventieth Birthday, J. Partial Differential Equations 21 (2008) 22-44. | MR | Zbl
, , ,[19] Global Well-Posedness and Scattering for the Energy-Critical, Defocusing Hartree Equation for Radial Data, J. Funct. Anal. 253 (2007) 605-627. | MR | Zbl
, , ,[20] Global Well-Posedness and Scattering for the Energy-Critical, Defocusing Hartree Equation in , arXiv:0707.3254.
, , ,[21] Global Well-Posedness and Scattering for the Mass-Critical Hartree Equation With Radial Data, J. Math. Pures Appl. 91 (2009) 49-79. | MR | Zbl
, , ,[22] Energy Scattering for Hartree Equations, Math. Res. Lett. 6 (1999) 107-118. | MR | Zbl
,[23] Nonlinear Scattering With Nonlocal Interactions, Comm. Math. Phys. 146 (1992) 259-275. | MR | Zbl
, ,[24] Multilinear Weighted Convolution of Functions, and Applications to Non-Linear Dispersive Equations, Amer. J. Math. 123 (2001) 839-908. | MR | Zbl
,[25] Nonlinear Dispersive Equations. Local and Global Analysis, CBMS Regional Conf. Ser. in Math., vol. 106, Amer. Math. Soc., 2006. | MR | Zbl
,[26] http://tosio.math.toronto.edu/wiki/index.php/Main_Page.
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