Gevrey regularity of the global attractor for the dissipative Zakharov system

Abstract

We study the dissipative case of the Zakharov system with periodic boundary conditions. We prove that this system has a strong solution and generate a dissipative dynamical system possessing a global compact attractor. Our main result is that this attractor belongs to some Gevrey class. This result means that the elements of the attractor are analytic functions of the spatial variable. The main corollary of this result is the existence of two determining nodes for this problem. It means that in the framework of Zakharov's model the propagation of Langmuir's waves in plasma can be completely determined from the measurements in two spatial points.

Acknowledgement

The author is grateful to Professor I. D. Chueshov for constant attention to this work.