Small data scattering for nonlinear Schrödinger equations (NLS), nonlinear wave equations (NLW), nonlinear Klein-Gordon equations (NLKG) with power type nonlinearities is studied in the scheme of Sobolev spaces on the whole space with order . The assumptions on the nonlinearities are described in terms of power behavior at zero and at infinity such as for NLS and NLKG, and for NLW.
@article{ASNSP_2002_5_1_2_435_0, author = {Nakamura, Makoto and Ozawa, Tohru}, title = {Small data scattering for nonlinear {Schr\"odinger} wave and {Klein-Gordon} equations}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {435--460}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 1}, number = {2}, year = {2002}, mrnumber = {1991146}, zbl = {1121.35086}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2002_5_1_2_435_0/} }
TY - JOUR AU - Nakamura, Makoto AU - Ozawa, Tohru TI - Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 435 EP - 460 VL - 1 IS - 2 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2002_5_1_2_435_0/ LA - en ID - ASNSP_2002_5_1_2_435_0 ER -
%0 Journal Article %A Nakamura, Makoto %A Ozawa, Tohru %T Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 435-460 %V 1 %N 2 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_2002_5_1_2_435_0/ %G en %F ASNSP_2002_5_1_2_435_0
Nakamura, Makoto; Ozawa, Tohru. Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 2, pp. 435-460. http://www.numdam.org/item/ASNSP_2002_5_1_2_435_0/
[1] “Interpolation Spaces”, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin-New York, 1976. | Zbl
- ,[2] “An Introduction to Nonlinear Schrödinger Equations”, Textos de Métodos Matemáticos 22, Instituto de Matemática, Rio de Janeiro, 1989.
,[3] Équation d'évolution avec non-linéarité logarithmique, Ann. Fac. Sci. Toulouse 2 (1980), 21-51. | Numdam | MR | Zbl
- ,[4] The Cauchy problem for the critical nonlinear Schrödinger equation in , Nonlinear Anal. 14 (1990), 807-836. | MR | Zbl
- ,[5] Generalized Strichartz inequalities for the wave equation, J. Funct. Anal. 133 (1995), 50-68. | MR | Zbl
- ,[6] The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z. 189 (1985), 487-505. | MR | Zbl
- ,[7] On nonlinear Schrödinger equations 67 (1995), 281-306. | MR | Zbl
,[8] Nonlinear Schrödinger equations, In: “Schrödinger Operators”, H. Holden - A. Jensen (eds.), Lecture Notes in Phys. 345, Springer, Berlin, 1989, pp. 218-263. | MR | Zbl
,[9] Endpoint Strichartz estimates, Amer. J. Math. 120 (1998), 955-980. | MR | Zbl
- ,[10] On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal. 130 (1995), 357-426. | MR | Zbl
- ,[11] Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations, preprint. | MR | Zbl
- - ,[12] The Cauchy problem for nonlinear Klein-Gordon equations in the Sobolev spaces, Publ. Res. Inst. Math. Sci. 37 (2001), 255-293. | MR | Zbl
- ,[13] The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space, Ann. Inst. H. Poincaré, Physique théorique 71 (1999), 199-215. | Numdam | MR | Zbl
- ,[14] Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces, Reviews in Math. Phys. 9 (1997), 397-410. | MR | Zbl
- ,[15] Solutions of semilinear Schrödinger equations in , Ann. Inst. H. Poincaré Physique théorique 67 (1997), 259-296. | Numdam | MR | Zbl
,[16] Nonlinear small data scattering for the wave and Klein-Gordon equation, Math. Z. 185 (1984), 261-270. | MR | Zbl
,[17] “Field Theory”, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1990. | MR | Zbl
,[18] Nonlinear scattering theory at low energy, J. Funct. Anal. 41 (1981), 110-133. | MR | Zbl
,[19] Nonlinear scattering theory at low energy: sequel, J. Funct. Anal. 43 (1981), 281-293. | MR | Zbl
,[20] “Theory of Function Spaces”, Birkhäuser, Basel, 1983. | MR | Zbl
,[21] Scattering of solutions of nonlinear Klein-Gordon equations in three space dimensions, J. Math. Soc. Japan 35 (1983), 521-538. | MR | Zbl
,[22] Scattering of solutions for critical and subcritical nonlinear Klein-Gordon equations in , Discrete Contin. Dynam. Systems 5 (1999), 753-763. | MR | Zbl
,