Global Solutions and Their Large-time Behavior of Cauchy Problem for Equations of Deep Water Type (Journal of Partial Differential Equations, 1996)
We consider the large time behavior of the global solution of the Cauchy problem for the equation of Benjamin-Ono type. A series of large-time global estimates for Cauchy problem arc constructed. By means of the obtained global estimates uniformly for 0 ≤ t < ∞, the attractors of the Cauchy problem for the mentioned nonlinear equations are considered. And also the dimensions of the global attractor are estimated.
Keywords: Large time behavior; Benjamin-Ono type equations; global attractor