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

Makoto Nakamura; Tohru Ozawa

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 2, page 435-460
  • ISSN: 0391-173X

Abstract

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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 ≤ p 1 ≤ p 2 ≤ 1 + 4 / ( n - 2 s ) for NLS and NLKG, and 1 + 4 / ( n - 1 ) ≤ p 1 ≤ p 2 ≤ 1 + 4 / ( n - 2 s ) for NLW.

How to cite

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Nakamura, Makoto, and Ozawa, Tohru. "Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.2 (2002): 435-460. <http://eudml.org/doc/84476>.

@article{Nakamura2002,
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 $\mathbb \{R\}^n$ with order $s&lt;n/2$. The assumptions on the nonlinearities are described in terms of power behavior $p_1$ at zero and $p_2$ at infinity such as $1+4/n\le p_1\le p_2\le 1+4/(n-2s)$ for NLS and NLKG, and $1+4/(n-1)\le p_1\le p_2\le 1+4/(n-2s)$ for NLW.},
author = {Nakamura, Makoto, Ozawa, Tohru},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {2},
pages = {435-460},
publisher = {Scuola normale superiore},
title = {Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations},
url = {http://eudml.org/doc/84476},
volume = {1},
year = {2002},
}

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
PB - Scuola normale superiore
VL - 1
IS - 2
SP - 435
EP - 460
AB - 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 $\mathbb {R}^n$ with order $s&lt;n/2$. The assumptions on the nonlinearities are described in terms of power behavior $p_1$ at zero and $p_2$ at infinity such as $1+4/n\le p_1\le p_2\le 1+4/(n-2s)$ for NLS and NLKG, and $1+4/(n-1)\le p_1\le p_2\le 1+4/(n-2s)$ for NLW.
LA - eng
UR - http://eudml.org/doc/84476
ER -

References

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