## Bounds in time for the Klein-Gordon-Schrödinger and the Zakharov system.(English)Zbl 1105.35115

The authors deal with the $$(2+1)$$-, $$(3+1)$$- and $$(4+1)$$-dimensional Klein-Gordon-Schrödinger system and $$(2+1)$$- and $$(3+1)$$-dimensional Zakharov system. It is shown that the spatial Sobolev norms of regular global solutions grow at most polynomially with a bound depending on the regularity class of the data. To this end the authors use the Fourier restriction norm method.

### MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B35 Stability in context of PDEs
Full Text: