Asymptotic behavior of compressible p-th power Newtonian fluid with large initial data

In this paper, we study a large time behavior of the global spherically or cylindrically symmetric solutions in H1H1 for the p-th power compressible Newtonian fluid in multi-dimension with large initial data. Precisely, if the initial data is spherically symmetric, the space dimension can be taken not less than two; on the other hand, if the initial data is cylindrically symmetric, the smallness of initial data is not needed. The main concern of the present paper is to investigate the exponential decay rate of a solution toward the stationary solution as time goes to infinity. We get the uniform positive lower and upper bounds of the density by using different methods.