Global existence and decay estimate of classical solutions to the compressible viscoelastic flows with self-gravitating

In this paper, we consider the initial value problem for the compressible viscoelastic flows with self-gravitating in Rⁿ(n≥ 3). Global existence and decay rates of classical solutions are established. The corresponding linear equations becomes two similar equations by using Hodge decomposition and then the solutions operator is derived. The proof is mainly based on the decay properties of the solutions operator and energy method. The decay properties of the solutions operator may be derived from the pointwise estimate of the solution operator to two linear wave equations.