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

Nakamura, Makoto; Ozawa, Tohru

Nakamura, Makoto ; Ozawa, Tohru

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

Abstract

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 1991146 | Zbl 1121.35086 | 1 citation in Numdam

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},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {2},
     year = {2002},
     pages = {435-460},
     zbl = {1121.35086},
     mrnumber = {1991146},
     language = {en},
     url = {http://www.numdam.org/item/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, Série 5, Volume 1 (2002) no. 2, pp. 435-460. http://www.numdam.org/item/ASNSP_2002_5_1_2_435_0/

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