Tohoku Mathematical Journal
2001
June
SECOND SERIES VOL. 53, NO. 2

Tohoku Math. J.
53 (2001), 285-303

Title REMARKS ON THE ENERGY SCATTERING FOR NONLINEAR KLEIN-GORDON AND SCHRÖDINGER EQUATIONS

Author Kenji Nakanishi

(Received August 4, 1999)
Abstract. We give an improved proof for the result established recently by the present author that the scattering operators are well-defined in the whole energy space for a class of nonlinear Klein-Gordon and Schrödinger equations in any spatial dimension. Using some Sobolev-type inequatilies, we can simplify and somewhat enhance the Morawetz-type estimates and thereby weaken the required repulsivity conditions.

2000 Mathematics Subject Classification. Primary 35P25; Secondary 35L70, 35Q55.

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