Higher regularity of global attractor for a damped Benjamin-Bona-Mahony equation on R

摘要

For one-dimensional damped Benjamin-Bona-Mahony equation, a recent result claimed that there exists a global attractor in H-1(R), in fact the attractor is smoother and it belongs to H3/2-epsilon (R) for every epsilon > 0. In this paper, by some techniques of harmonic analysis, we first show that the solution operator of one-dimensional damped BBM equation is asymptotically compact, then we give the existence of global attractor in H-1(R) boolean AND W-1,W- p(R) (2 <= p < infinity). Finally, we obtain the higher regularity of the global attractor, it is in fact bounded in H-2(R) boolean AND W-2,W- p(R).