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

Makoto Nakamura, Tohru Ozawa (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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 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.

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