Evolution Equations and Control Theory (EECT)

Semi-weak well-posedness and attractors for 2D Schrödinger-Boussinesq equations

Pages: 57 - 80, Volume 1, Issue 1, June 2012      doi:10.3934/eect.2012.1.57

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Igor Chueshov - Kharkov National Universit, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkov, Ukraine (email)
Alexey Shcherbina - Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody Sq. 61077 Kharkov, Ukraine (email)

Abstract: We deal with an initial boundary value problem for the Schrödinger-Boussinesq system arising in plasma physics in two-dimensional domains. We prove the global Hadamard well-posedness of this problem (with respect to the topology which is weaker than topology associated with the standard variational (weak) solutions) and study properties of the solutions. In the dissipative case the existence of a global attractor is established.

Keywords:  2D Schrödinger-Boussinesq models, weak and strong solutions, global attractors.
Mathematics Subject Classification:  Primary: 35Q40; Secondary: 35B40, 37L05, 37L30.

Received: October 2011;      Revised: January 2012;      Available Online: March 2012.