Bounds in time for the Klein-Gordon-Schroedinger and the Zakharov system
  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. 
Axel Gruenrock and Hartmut Pecher