Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations

Nakamura, Makoto; Ozawa, Tohru

Geodesic

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Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations

Nakamura, Makoto ; Ozawa, Tohru

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 2, pp. 435-460

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Résumé

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 $ℝ^{n}$ with order $s < n / 2$ . The assumptions on the nonlinearities are described in terms of power behavior $p_{1}$ at zero and $p_{2}$ at infinity such as $1 + 4 / n \leq p_{1} \leq p_{2} \leq 1 + 4 / (n - 2 s)$ for NLS and NLKG, and $1 + 4 / (n - 1) \leq p_{1} \leq p_{2} \leq 1 + 4 / (n - 2 s)$ for NLW.

MR Zbl

Classification : 35L70

@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://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_435_0/}
}

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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, Série 5, Tome 1 (2002) no. 2, pp. 435-460. http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_435_0/