Solutions of semilinear Schrödinger equations in H s
Annales de l'I.H.P. Physique théorique, Volume 67 (1997) no. 3, pp. 259-296.
@article{AIHPA_1997__67_3_259_0,
     author = {Pecher, Hartmut},
     title = {Solutions of semilinear {Schr\"odinger} equations in $H^s$},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {259--296},
     publisher = {Gauthier-Villars},
     volume = {67},
     number = {3},
     year = {1997},
     zbl = {0888.35101},
     mrnumber = {1472820},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1997__67_3_259_0/}
}
TY  - JOUR
AU  - Pecher, Hartmut
TI  - Solutions of semilinear Schrödinger equations in $H^s$
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1997
DA  - 1997///
SP  - 259
EP  - 296
VL  - 67
IS  - 3
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1997__67_3_259_0/
UR  - https://zbmath.org/?q=an%3A0888.35101
UR  - https://www.ams.org/mathscinet-getitem?mr=1472820
LA  - en
ID  - AIHPA_1997__67_3_259_0
ER  - 
%0 Journal Article
%A Pecher, Hartmut
%T Solutions of semilinear Schrödinger equations in $H^s$
%J Annales de l'I.H.P. Physique théorique
%D 1997
%P 259-296
%V 67
%N 3
%I Gauthier-Villars
%G en
%F AIHPA_1997__67_3_259_0
Pecher, Hartmut. Solutions of semilinear Schrödinger equations in $H^s$. Annales de l'I.H.P. Physique théorique, Volume 67 (1997) no. 3, pp. 259-296. http://archive.numdam.org/item/AIHPA_1997__67_3_259_0/

[1] J. Bergh and J. Löfström, Interpolation spaces, Springer, Berlin-Heidelberg-New York, 1976. | MR | Zbl

[2] Th Cazenave and F.B. Weissler, The Cauchy problem for the critical nonlinear Schrödinger equation in Hs, Nonlinear Analysis, Vol. 14, 1990, pp. 807-836. | MR | Zbl

[3] J. Ginibre, T. Ozawa and G. Velo, On the existence of the wave operators for a class of nonlinear Schrödinger equations. Ann. Inst. H. Poincaré, Phys. Theor., Vol. 60, 1994, pp. 211-239. | Numdam | MR | Zbl

[4] J. Ginibre and G. Velo, The global Cauchy problem for the non linear Schrödinger equation revisited, Ann. Inst. H. Poincaré, Analyse non linéaire, Vol. 2, 1985, pp. 309-327. | Numdam | MR | Zbl

[5] T. Kato, On nonlinear Schrödinger equations. Ann. Inst. H. Poincaré, Phys. Theor., Vol. 46, 1987, pp. 113-129. | Numdam | MR | Zbl

[6] T. Kato, On nonlinear Schrödinger equations II. Hs-solutions and unconditional well-posedness. J. d'Anal. Math., Vol. 67, 1995, pp. 281-306. | MR | Zbl

[7] H. Lindblad and C.D. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J. Functional Analysis, Vol. 130, 1995, pp. 357-426. | MR | Zbl

[8] J.L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Etudes Scientifiques. Publ. Math., Vol. 19, 1964, pp. 5-68. | Numdam | MR | Zbl

[9] H. Pecher, Local solutions of semilinear wave equations in Hs+1. Math. Meth. in the Appl. Sciences, Vol. 19, 1996, pp. 145-170. | MR | Zbl

[10] J. Peetre, Über den Durchschnitt von Interpolationsräumen. Arch. Math. (Basel), Vol. 25, 1974, pp. 511-513. | MR | Zbl

[11] J. Schwartz, A remark on inequalities of Calderon-Zygmund type for vector-valued functions, Comm. Pure Appl. Math., Vol. 14, 1961, pp. 785-799. | MR | Zbl

[12] W.A. Strauss, Nonlinear wave equations. CBMS Lecture Notes, No. 73, American Math. Society, Providence, RI, 1989. | MR

[13] Triebel H., Interpolation theory, function spaces, differential operators. North-Holland, Amsterdam-New York-Oxford, 1978. | Zbl

[14] K. Yajima, Existence of solutions for Schrödinger evolution equations. Comm. Math. Phys., Vol. 110, 1987, pp. 415-426. | MR | Zbl