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Bounds in time for the Klein-Gordon-Schroedinger and the Zakharov system

Axel Gruenrock·Hartmut Pecher
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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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Axel Gruenrock, Hartmut Pecher. 2004-03-04. Bounds in time for the Klein-Gordon-Schroedinger and the Zakharov system. https://arxiv.org/abs/math/0401352

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