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

Abstract

For one-dimensional damped Benjamin–Bona–Mahony equation, a recent result claimed that there exists a global attractor in , in fact the attractor is smoother and it belongs to for every . 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 . Finally, we obtain the higher regularity of the global attractor, it is in fact bounded in .