Solutions of semilinear Schrödinger equations in H s
Annales de l'I.H.P. Physique théorique, Volume 67 (1997) no. 3, p. 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},
     publisher = {Gauthier-Villars},
     volume = {67},
     number = {3},
     year = {1997},
     pages = {259-296},
     zbl = {0888.35101},
     mrnumber = {1472820},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/AIHPA_1997__67_3_259_0/

[1] J. Bergh and J. Löfström, Interpolation spaces, Springer, Berlin-Heidelberg-New York, 1976. | MR 482275 | Zbl 0344.46071

[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 1055532 | Zbl 0706.35127

[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 1270296 | Zbl 0808.35136

[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 801582 | Zbl 0586.35042

[5] T. Kato, On nonlinear Schrödinger equations. Ann. Inst. H. Poincaré, Phys. Theor., Vol. 46, 1987, pp. 113-129. | Numdam | MR 877998 | Zbl 0632.35038

[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 1383498 | Zbl 0848.35124

[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 1335386 | Zbl 0846.35085

[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 165343 | Zbl 0148.11403

[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 1368792 | Zbl 0845.35069

[10] J. Peetre, Über den Durchschnitt von Interpolationsräumen. Arch. Math. (Basel), Vol. 25, 1974, pp. 511-513. | MR 383103 | Zbl 0293.46025

[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 143031 | Zbl 0106.08104

[12] W.A. Strauss, Nonlinear wave equations. CBMS Lecture Notes, No. 73, American Math. Society, Providence, RI, 1989. | MR 1032250

[13] Triebel H., Interpolation theory, function spaces, differential operators. North-Holland, Amsterdam-New York-Oxford, 1978. | Zbl 0387.46032

[14] K. Yajima, Existence of solutions for Schrödinger evolution equations. Comm. Math. Phys., Vol. 110, 1987, pp. 415-426. | MR 891945 | Zbl 0638.35036