On 2D Zakharov system in a bounded domain. (English) Zbl 1212.35361

The paper deals with initial boundary-value problems for the Zakharov system arising in plasma physics in two-dimensional domains under various boundary conditions. The global well-posedness of these problems in some Sobolev-type classes is proved and properties of the solutions studied. In the dissipative case the existence of a global attractor is established.


35Q35 PDEs in connection with fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems