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Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system

Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system

It is well known that the coupled Klein-Gordon-Schrödinger system possesses a compact global attractor into a suitable energy space. We prove the asymptotical smoothing effect for this system, i.e., we prove that the attractor is in fact embedded into a smaller energy space.