Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems

verfasst von: Yuming Qin, Lan Huang

Verlag: Springer Basel

Buchreihe : Frontiers in Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressible Navier-Stokes equations, and liquid crystal system. It summarizes recently published research by the authors and their collaborators, but also includes new and unpublished material. All models under consideration are built on compressible equations and liquid crystal systems. This type of partial differential equations arises not only in many fields of mathematics, but also in other branches of science such as physics, fluid dynamics and material science.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Global Existence of Spherically Symmetric Solutions for Nonlinear Compressible Non-autonomous Navier-Stokes Equations

Abstract

This chapter concerns the global existence of spherically symmetric solutions for nonlinear compressible non-autonomous Navier-Stokes equations of an initial boundary value problem with an external force and a heat source in bounded annular domains\( {G_n}=\{r\in\mathbb{R}^n:{a\leq r \leq b}\}\,{\rm in}\, {\mathbb{R}^n} \,(1\leq n \leq 3).\)

Yuming Qin, Lan Huang

Chapter 2. Global Existence and Exponential Stability for a Real Viscous Heat-conducting Flow with Shear Viscosity

Abstract

In this chapter we shall study the global existence and exponential stability of weak solutions for a real viscous compressible heat-conducting flow between two horizontal plates.

Yuming Qin, Lan Huang

Chapter 3. Regularity and Exponential Stability of the pth Power Newtonian Fluid in One Space Dimension

Abstract

In this chapter, we are interested in the regularity and exponential stability of solutions in H ⁱ (i = 2,4) for a pth power Newtonian fluid undergoing one-dimensional longitudinal motions.

Yuming Qin, Lan Huang

Chapter 4. Global Existence and Exponential Stability for the pth Power Viscous Reactive Gas

Abstract

In this chapter, we prove the global existence and exponential stability of solutions in H ⁱ(i= 2,4) for the compressible Navier-Stokes equations, which arise in the study of a thermal explosion and describe the dynamic combustion for a reactive Newtonian fluid, confined between two infinite parallel plates.

Yuming Qin, Lan Huang

Chapter 5. On a 1D Viscous Reactive and Radiative Gas with First-order Arrhenius Kinetics

Abstract

In this chapter, we establish the global existence and exponential stability of solutions in H ⁱ (i = 1,2,4) for a Stefan-Boltzmann model of a viscous, reactive and radiative gas with first-order Arrhenius kinetics in a bounded interval. In so doing we describe the classical stellar evolution [11] of a finite mass of a heat-conducting viscous reactive fluid in local equilibrium with thermal radiation: pressure, internal energy and thermal conductivity have Stefan-Boltzmann radiative contributions. In order to mimic chemical exchanges inside the fluid, we may consider a simple reacting process with a first-order kinetics, commonly used in combustion theory [12]. The results of this chapter are chosen from [63].

Yuming Qin, Lan Huang

Backmatter

Titel: Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems
verfasst von: Yuming Qin
Lan Huang
Verlag: Springer Basel
Electronic ISBN: 978-3-0348-0280-2
Print ISBN: 978-3-0348-0279-6
DOI: https://doi.org/10.1007/978-3-0348-0280-2