Long time dynamics for a damped Benjamin–Bona–Mahony equation in low regularity spaces

Long time behavior of solutions for a damped BBM equation in low regularity space is investigated. By the II-method and high–low frequency decomposition, we prove the existence of a global attractor in L2L2 if the force belongs to L2L2. Moreover, we show that the global attractor has finite fractal dimension in the sharp regularity space H2H2.