Bounds in time for the Klein-Gordon-Schroedinger and the Zakharov system
Axel Gruenrock, Hartmut Pecher
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-Schroedinger system and the (2+1) and (3+1)-dimensional Zakharov system grow at most polynomially with the bound depending on the regularity class of the data. The proof uses the Fourier restriction norm method.
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