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Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system with cubic nonlinearities in $\mathbb{R}^2$

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  • we prove the existence of a global attractor to dissipative Klein-Gordon-Schrödinger (KGS) system with cubic nonlinearities in $H^1({\mathbb R}^2)\times H^1({\mathbb R}^2)\times L^2({\mathbb R}^2)$ and more particularly that this attractor is in fact a compact set of $H^2({\mathbb R}^2)\times H^2({\mathbb R}^2)\times H^1({\mathbb R}^2)$.
    Mathematics Subject Classification: Primary: 37L30, 37L50; Secondary: 35 A01.

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