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.

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 $1+4/n\le p_1\le p_2\le 1+4/(n-2s)$ for NLS and NLKG, and $1+4/(n-1)\le p_1\le p_2\le 1+4/(n-2s)$ for NLW.

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