Scattering theory for the Schrödinger equation in some external time-dependent magnetic fields

Journal of Differential Equations

Volumn 215, Issue 1, 2005, Pages 108-177

  Ginibre, Jean ^a   Velo, G ^b  

^a UNIVERSITÉ PARIS SUD   (France)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Scattering theory; Schr dinger equation; Time dependent magnetic fields

Indexed keywords

EID: 18144398224     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.10.024     Document Type: Article

References (17)

1. J. Bergh J. Löfström Interpolation Spaces 1976 Springer Berlin
2. F. Colombini N. Lerner Uniqueness of continuous solutions for BV vector fields Duke Math. J. 111 2002 357-384
3. R. Di Perna P.L. Lions Ordinary differential equations, transport theory and Sobolev spaces Invent. Math. 98 1989 511-547
4. J. Ginibre G. Velo Generalized Strichartz inequalities for the wave equation J. Funct. Anal. 133 1995 50-68
5. J. Ginibre G. Velo Long range scattering and modified wave operators for the Wave-Schrödinger system Ann. H.P. 3 2002 537-612
6. J. Ginibre G. Velo Long range scattering and modified wave operators for the Wave-Schrödinger system II Ann. H.P. 4 2003 973-999
7. J. Ginibre G. Velo Long range scattering and modified wave operators for the Maxwell-Schrödinger system I. The case of vanishing asymptotic magnetic field Comm. Math. Phys. 236 2003 395-448
8. L. Hörmander, The Analysis of Partial Differential Operators, vol. I, Springer, Berlin, 1983.
9. J.L. Lions Quelques méthodes de résolution des problèmes aux limites non linéaires 1968 Dunod et Gauthier-Villars Paris
10. M. Nakamura, T. Wada, Local well-posedness for the Maxwell-Schrödinger equation, preprint math. AP/0304486 (2003).
11. M. Reed, B. Simon, Methods of Modern Mathematical Physics, Functional Analysis, vol. I, Academic Press, New York, 1972.
12. A. Shimomura Modified wave operators for the coupled Wave-Schrödinger equations in three space dimensions Discrete Cont. Dyn. Systems 9 2003 1571-1586
13. A. Shimomura Modified wave operators for Maxwell-Schrödinger equations in three space dimensions Ann. H.P. 4 2003 661-683
14. W. Strauss, Non Linear Wave Equations, CMBS Lecture Notes, vol. 73, American Mathematical Society, Providence, RI, 1989.
15. H. Triebel Theory of Function Spaces 1983 Birkhäuser Basel
16. Y. Tsutsumi Global existence and asymptotic behavior for the Maxwell-Schrödinger system in three space dimensions Comm. Math. Phys. 151 1993 543-576
17. K. Yajima Schrödinger evolution equations with magnetic fields J. Anal. Math. 56 1991 29-76