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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
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