𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the uniqueness of the solution of the two-dimensional Navier–Stokes equation with a Dirac mass as initial vorticity

✍ Scribed by Isabelle Gallagher; Thierry Gallay; Pierre-Louis Lions

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
149 KB
Volume
278
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We propose two different proofs of the fact that Oseen's vortex is the unique solution of the two‐dimensional Navier–Stokes equation with a Dirac mass as initial vorticity. The first argument, due to C. E. Wayne and the second named author, is based on an entropy estimate for the vorticity equation in self‐similar variables. The second proof is new and relies on symmetrization techniques for parabolic equations. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 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 👁 2 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 domain dependence of solutions to
On the domain dependence of solutions to the Navier–Stokes equations of a two-dimensional compressible flow
✍ Fei Jiang; Zhong Tan 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 145 KB 👁 2 views

## 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

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