The global attractor of the viscous damped forced Ostrovsky equation

Abstract

The existence of the global attractor of the viscous damped forced Ostrovsky equation in L ̃ 2 ( R ) is proved. An asymptotic smoothing effect of the equation is also shown, namely, that for the forces in L ̃ 2 ( R ) , the global attractor in L ̃ 2 ( R ) is actually a compact set in H ̃ 3 ( R ) . The energy equation method is used in conjunction with a suitable splitting of the solutions; the regularization properties of the equation in the context of Bourgain spaces are extensively exploited.