Solutions of semilinear Schrödinger equations in H s

Hartmut Pecher

Annales de l'I.H.P. Physique théorique (1997)

  • Volume: 67, Issue: 3, page 259-296
  • ISSN: 0246-0211

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Pecher, Hartmut. "Solutions of semilinear Schrödinger equations in $H^s$." Annales de l'I.H.P. Physique théorique 67.3 (1997): 259-296. <http://eudml.org/doc/76770>.

@article{Pecher1997,
author = {Pecher, Hartmut},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {nonlinear Schrödinger equation; local problem; global small data problem; Besov spaces; Sobolev spaces},
language = {eng},
number = {3},
pages = {259-296},
publisher = {Gauthier-Villars},
title = {Solutions of semilinear Schrödinger equations in $H^s$},
url = {http://eudml.org/doc/76770},
volume = {67},
year = {1997},
}

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
PB - Gauthier-Villars
VL - 67
IS - 3
SP - 259
EP - 296
LA - eng
KW - nonlinear Schrödinger equation; local problem; global small data problem; Besov spaces; Sobolev spaces
UR - http://eudml.org/doc/76770
ER -

References

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  1. [1] J. Bergh and J. Löfström, Interpolation spaces, Springer, Berlin-Heidelberg-New York, 1976. Zbl0344.46071MR482275
  2. [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. Zbl0706.35127MR1055532
  3. [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. Zbl0808.35136MR1270296
  4. [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. Zbl0586.35042MR801582
  5. [5] T. Kato, On nonlinear Schrödinger equations. Ann. Inst. H. Poincaré, Phys. Theor., Vol. 46, 1987, pp. 113-129. Zbl0632.35038MR877998
  6. [6] T. Kato, On nonlinear Schrödinger equations II. Hs-solutions and unconditional well–posedness. J. d'Anal. Math., Vol. 67, 1995, pp. 281-306. Zbl0848.35124MR1383498
  7. [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. Zbl0846.35085MR1335386
  8. [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. Zbl0148.11403MR165343
  9. [9] H. Pecher, Local solutions of semilinear wave equations in Hs+1. Math. Meth. in the Appl. Sciences, Vol. 19, 1996, pp. 145-170. Zbl0845.35069MR1368792
  10. [10] J. Peetre, Über den Durchschnitt von Interpolationsräumen. Arch. Math. (Basel), Vol. 25, 1974, pp. 511-513. Zbl0293.46025MR383103
  11. [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. Zbl0106.08104MR143031
  12. [12] W.A. Strauss, Nonlinear wave equations. CBMS Lecture Notes, No. 73, American Math. Society, Providence, RI, 1989. MR1032250
  13. [13] Triebel H., Interpolation theory, function spaces, differential operators. North-Holland, Amsterdam-New York-Oxford, 1978. Zbl0387.46032
  14. [14] K. Yajima, Existence of solutions for Schrödinger evolution equations. Comm. Math. Phys., Vol. 110, 1987, pp. 415-426. Zbl0638.35036MR891945

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