It is shown that the spatial Sobolev norms of regular global solutions of the (2 + 1), (3 + 1) and (4 + 1)-dimensional Klein-Gordon-Schr\"odinger system and the (2+1) and (3+1)-dimensional Zakharov system grow at most polynomially with a bound depending on the regularity class of the data. The proof uses the Fourier restriction norm method.
Publié le : 2006-02-15
Classification:
Klein-Gordon-Schr\"odinger,
growth bounds,
global solutions,
35L05,
35Q55
@article{1285766303,
author = {GR\"UNROCK, Axel and PECHER, Hartmut},
title = {Bounds in time for the Klein-Gordon-Schr\"odinger and the Zakharov system},
journal = {Hokkaido Math. J.},
volume = {35},
number = {1},
year = {2006},
pages = { 139-153},
language = {en},
url = {http://dml.mathdoc.fr/item/1285766303}
}
GR\"UNROCK, Axel; PECHER, Hartmut. Bounds in time for the Klein-Gordon-Schr\"odinger and the Zakharov system. Hokkaido Math. J., Tome 35 (2006) no. 1, pp. 139-153. http://gdmltest.u-ga.fr/item/1285766303/