Remarks on the energy scattering for nonlinear Klein-Gordon and Schrödinger equations

Nakanishi, Kenji

Tohoku Math. J. (2), Tome 53 (2001) no. 4, p. 285-303 / Harvested from Project Euclid

Résumé

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.

Publié le : 2001-05-14
Classification: 35Q55, 35L70, 35P25

@article{1178207482,
     author = {Nakanishi, Kenji},
     title = {Remarks on the energy scattering for nonlinear Klein-Gordon and Schr\"odinger equations},
     journal = {Tohoku Math. J. (2)},
     volume = {53},
     number = {4},
     year = {2001},
     pages = { 285-303},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1178207482}
}

Nakanishi, Kenji. Remarks on the energy scattering for nonlinear Klein-Gordon and Schrödinger equations. Tohoku Math. J. (2), Tome 53 (2001) no. 4, pp.  285-303. http://gdmltest.u-ga.fr/item/1178207482/