Global existence and asymptotic behavior for the compressible Navier-Stokes equations with a non-autonomous external force and a heat source

摘要

In this paper, we prove the global existence and asymptotic behavior, as time tends to infinity of solutions in H-i (i = 1, 2) to the initial boundary value problem of the compressible Navier-Stokes equations of one-dimensional motion of a viscous heat-conducting gas in a bounded region with a non-autonomous external force and a heat source. Some new ideas and more delicate estimates are used to prove these results.