𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the domain dependence of solutions to the Navier–Stokes equations of a two-dimensional compressible flow

✍ Scribed by Fei Jiang; Zhong Tan

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
145 KB
Volume
32
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We consider the Navier–Stokes equations for compressible, barotropic flow in two space dimensions, with pressure satisfying p(ϱ)=__a__ϱlog^d^(ϱ) for large ϱ, here d>1 and a>0. After introducing useful tools from the theory of Orlicz spaces, we prove a compactness result for the solution set of the equations with respect to the variation of the underlying bounded spatial domain. Especially, we get a general existence theorem for the system in question with no restrictions on smoothness of the bounded spatial domain. Copyright © 2009 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

On the existence of solutions to the Nav
On the existence of solutions to the Navier–Stokes equations of a two-dimensional compressible flow
✍ Radek Erban 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 218 KB 👁 1 views

## Abstract We consider the Navier–Stokes equations for compressible, barotropic flow in two space dimensions. We introduce useful tools from the theory of Orlicz spaces. Then we prove the existence of globally defined finite energy weak solutions for the pressure satisfying __p__(__ϱ__) = __aϱ__lo

On the existence of solutions to the Nav
On the existence of solutions to the Navier–Stokes–Poisson equations of a two-dimensional compressible flow
✍ Yinghui Zhang; Zhong Tan 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 216 KB 👁 1 views

## Abstract In this paper, we consider the Navier–Stokes–Poisson equations for compressible, barotropic flow in two space dimensions. We introduce useful tools from the theory of Orlicz spaces. Then we prove the existence of globally defined finite energy weak solutions for the pressure satisfying

On the domain dependence of solutions to
On the domain dependence of solutions to the compressible Navier–Stokes equations of a barotropic fluid
✍ Eduard Feireisl; Antonín Novotný; Hana Petzeltová 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 201 KB 👁 2 views

## Abstract We prove a general compactness result for the solution set of the compressible Navier–Stokes equations with respect to the variation of the underlying spatial domain. Among various corollaries, we then prove a general existence theorem for the system in question with no restrictions on

Stability of weak solutions to the compr
Stability of weak solutions to the compressible Navier–Stokes equations in bounded annular domains
✍ Jishan Fan; Hongjun Gao 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 143 KB

## Abstract We prove the Lipschitz continuous dependence on initial data of global spherically symmetric weak solutions to the Navier–Stokes equations of a viscous polytropic ideal gas in bounded annular domains with the initial data in the Lebesgue spaces. Copyright © 2007 John Wiley & Sons, Ltd.

Blowup of smooth solutions to the compre
Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density
✍ Zhouping Xin 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 194 KB 👁 2 views

We present a sufficient condition on the blowup of smooth solutions to the compressible Navier-Stokes equations in arbitrary space dimensions with initial density of compact support. As an immediate application, it is shown that any smooth solutions to the compressible Navier-Stokes equations for po