[1] I. Bejenaru, and D. Tataru. Global wellposedness in the energy space for the Maxwell–Schr¨odinger system.
Comm. Math. Phys., 288(1):145–198, 2009.
[2] J. Ginibre, and T. Ozawa. Long range scattering for nonlinear Schr¨odinger and Hartree equations in
space dimension n ≥ 2. Comm. Math. Phys., 151(3):619–645, 1993.
[3] J. Ginibre, and G. Velo. Long range scattering and modified wave operators for some Hartree type
equations I. Rev. Math. Phys., 12(3):361–429, 2000.
[4] J. Ginibre, and G. Velo. Long range scattering and modified wave operators for some Hartree type
equations II. Ann. Henri Poincar´e, 1(4):753–800, 2000.
[5] J. Ginibre, and G. Velo. Long range scattering and modified wave operators for some Hartree type
equations III. Gevrey spaces and low dimensions. J. Differential Equations, 175(2):415–501, 2001.
[6] J. Ginibre, and G. Velo. Long range scattering and modified wave operators for the Wave–Schr¨odinger
system I. Ann. Henri Poincar´e, 3(3):537–612, 2002.
[7] J. Ginibre, and G. Velo. Long range scattering and modified wave operators for the Wave–Schr¨odinger
system II. Ann. Henri Poincar´e, 4(5):973–999, 2003.
[8] J. Ginibre, and G. Velo. Long range scattering and modified wave operators for the Wave–Schr¨odinger
system III. Dyn. Partial Differ. Equ., 2(2):101–125, 2005.
[9] J. Ginibre, and G. Velo. Long range scattering and modified wave operators for the Maxwell–Schr¨odinger
system I. The case of vanishing asymptotic magnetic field. Comm. Math. Phys., 236(3):395–448, 2003.
[10] J. Ginibre, and G. Velo. Scattering theory for the Schr¨odinger equation in some external time dependent
magnetic fields. J. Differential Equations, 215(1):108–177, 2005.
[11] J. Ginibre, and G. Velo. Long range scattering for the Wave–Schr¨odinger system with large wave data
and small Schr¨
odinger data. Hokkaido Math. J., 35(2):261–287, 2006.
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[12] J. Ginibre, and G. Velo. Long range scattering for the Maxwell–Schr¨odinger system with large magnetic
field data and small Schr¨
odinger data. Publ. Res. Inst. Math. Sci., 42(2):421–459, 2006.
[13] J. Ginibre, and G. Velo. Long range scattering and modified wave operators for the Maxwell–Schr¨odinger
system II. The General case. Ann. Henri Poincar´e, 8(5):917–994, 2007.
[14] Y. Guo, K. Nakamitsu, and W. Strauss. Global finite energy solutions of the Maxwell–Schr¨odinger system.
Comm. Math. Phys., 170(1):181–196, 1995.
[15] N. Hayashi, and P. I. Naumkin. Domain and range of the modified wave operator for Schr¨odinger equations
with a critical nonlinearity. Comm. Math. Phys., 267(1):477–492, 2006.
[16] M. Nakamitsu, and M. Tsutsumi. The Cauchy problem for the coupled Maxwell–Schr¨odinger equations.
J. Math. Phys., 27(1):211–216, 1986.
[17] M. Nakamura, and T. Wada. Local wellposedness for the Maxwell–Schr¨odinger equations. Math. Ann.,
332(3):565–604, 2005.
[18] M. Nakamura, and T. Wada. Global existence and uniqueness of solutions to the Maxwell–Schr¨odinger
equations. Comm. Math. Phys., 276(2):315–339, 2007.
[19] K. Nakanishi. Modified wave operators for the Hartree equation with data, image and convergence in the
same space. Commun. Pure Appl. Anal., 1(2):237–252, 2002.
[20] K. Nakanishi. Modified wave operators for the Hartree equation with data, image and convergence in the
same space II. Ann. Henri Poincar´e, 3(3):503–535, 2002.
[21] T. Ozawa. Long range scattering for nonlinear Schr¨odinger equations in one space dimension. Comm.
Math. Phys., 139(3):479–493, 1991.
[22] T. Ozawa, and Y. Tsutsumi. Asymptotic behavior of solutions for the coupled Klein–Gordon–Schr¨odinger
equations. Spectral and scattering theory and applications, Adv. Stud. Pure Math., 23, 295–305, 1994.
[23] A. Shimomura. Scattering theory for the coupled Klein–Gordon–Schr¨odinger equations in two space
dimensions I. J. Math. Sci. Univ. Tokyo, 10(4):661–685, 2003.
[24] A. Shimomura. Scattering theory for the coupled Klein–Gordon–Schr¨odinger equations in two space
dimensions II. Hokkaido Math. J., 34(2):405–433, 2005.
[25] A. Shimomura. Modified wave operators for the coupled Wave–Schr¨odinger equations in three space
dimensions. Discrete Contin. Dyn. Syst., 9(6):1571–1586, 2003.
[26] A. Shimomura. Modified wave operators for Maxwell–Schr¨odinger equations in three space dimensions.
Ann. Henri Poincar´e, 4(4):661–683, 2003.
[27] W. Strauss. Non linear Wave Equations. CMBS Lecture notes 73, Am. Math. Soc., Providence, 1989.
[28] Y. Tsutsumi. Global existence and asymptotic behavior of solutions for the Maxwell–Schr¨odinger equations in three space dimensions. Comm. Math. Phys., 151(3):543–576, 1993.
[29] T. Wada. Smoothing effects for Schr¨
odinger equations with electro-magnetic potentials and applications
to the Maxwell–Schr¨
odinger equations. J. Funct. Anal., 263(1):1–24, 2012.
School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary
Sciences, Northeast Normal University, Changchun, Jilin 130024, PR China
LONG RANGE SCATTERING FOR THE MAXWELL–SCHRODINGER
SYSTEM
61
Double Degree Program, Mathematics Course, Interdisciplinary Graduate School of Science and Engineering, Shimane University, Matsue 690-8504, Japan
E-mail address: liuy694@nenu.edu.cn
Department of Mathematics, Shimane University, Matsue 690-8504, Japan
E-mail address: wada@riko.shimane-u.ac.jp
...