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

Igor Chueshov; Alexey Shcherbina

doi:10.3934/eect.2012.1.57

Article Contents

2012, Volume 1, Issue 1: 57-80. Doi: 10.3934/eect.2012.1.57

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

Igor Chueshov^1, and
Alexey Shcherbina^2,

1.
Kharkov National Universit, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkov
2.
Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody Sq. 61077 Kharkov

Received: September 30, 2011

Revised: December 31, 2011

Published: May 2012

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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.

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Mathematics Subject Classification: Primary: 35Q40; Secondary: 35B40, 37L05, 37L30.

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