Compressible Navier-Stokes Equations With A Non-autonomous External Force And A Heat Source

In this paper, we study the global existence and asymptotic behavior of solutions in H~4 of problem:which is one-dimensional compressible Navier-Stokes equations with a non-autonomous external force and a heat source. It describes a motion of a viscous heat conducting gas in a bounded domain.There are three chapters in this thesis. In Chapter 1, we introduce the background and present research situation, the problem and the method under consideration in this thesis; and we introduce some notations and the main results. In Chapter 2, we will prove Theorem 1, that is the proof of global existence. In Chapter 3, we will prove the exponential stability result in Theorem 2.