Global existence and asymptotic behavior of solution for the Rosenau equation with hydrodynamical damped term

We consider the Cauchy problem for Rosenau equation with hydrodynamical damped term in n-dimensional space. Under smallness condition on the initial data, we prove the global existence and asymptotic behavior of the solution in the time-weighted Sobolev spaces by the contraction mapping principle. (c) 2013 Elsevier Inc. All rights reserved.