Hokkaido Mathematical Journal

GR\"UNROCK Axel, PECHER Hartmut,

Bounds in time for the Klein-Gordon-Schr\"odinger and the Zakharov system.

Hokkaido Mathematical Journal, 35 (2006) pp.139-153

Fulltext

PDF

Abstract

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.

MSC(Primary)35L05
MSC(Secondary)35Q55
Uncontrolled KeywordsKlein-Gordon-Schr\"odinger, growth bounds, global solutions