# American Institute of Mathematical Sciences

2005, 2005(Special): 824-832. doi: 10.3934/proc.2005.2005.824

## On the global attractor for the damped Benjamin-Bona-Mahony equation

 1 Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence, KS 66045-7523, United States

Received  September 2004 Revised  April 2005 Published  September 2005

We present a new necessary and sufficient condition to verify the asymptotic compactness of an evolution equation defined in an unbounded domain, which involves the Littlewood-Paley projection operators. We then use this condition to prove the existence of an attractor for the damped \bbme in the phase space $H^1({\bf R})$ by showing the solutions are point dissipative and asymptotically compact. Moreover the attractor is in fact smoother and it belongs to $H^{3/2-\ve}$ for every $\ve>0$.
Citation: Milena Stanislavova. On the global attractor for the damped Benjamin-Bona-Mahony equation. Conference Publications, 2005, 2005 (Special) : 824-832. doi: 10.3934/proc.2005.2005.824
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