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.
Citation
Kenji Nakanishi. "Remarks on the energy scattering for nonlinear Klein-Gordon and Schrödinger equations." Tohoku Math. J. (2) 53 (2) 285 - 303, 2001. https://doi.org/10.2748/tmj/1178207482
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