Global Existence For A Non-Monotone Fluid In One Dimension In H～2: The Positive Temperature Case

We consider a one-dimensional continuous model of nutron star, described by a com-pressible Navier-Stokes system with a non-monotone equation of state, due to the e?ectiveSkyrme nuclear interaction between particles.We will show that, despite a possible destabilizing in?uence of the pressure, which isnon-monotone and not always positive, the presence of viscosity and a su?cient thermaldissipation describe the global existence of solutions with a mixed free boundary problemfor our model. There are two chapters in this dissertation.The physical background to our model is described in the introduction. In the firstchapter, we not only simply introduce the main result, some notations and the qualitativeproperties of the state equations, but also describe some results related to our model.The second chapter is the most important part. In this chapter, based on the Lemma 2.1and some familiar important inequalities, we get some estimates by energy methods andcombine it with the Lemma 2.1 , then we obtain the global existence of solutions to ourmodel with a mixed free boundary problem.In addition, we give some important inequalities which have been used frequently inthis dissertation.