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.
"Bounds in time for the Klein-Gordon-Schr\"odinger and the Zakharov system." Hokkaido Math. J. 35 (1) 139 - 153, February 2006. https://doi.org/10.14492/hokmj/1285766303