𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Possible Singular Solutions to the Navier — Stokes Equations

✍ Scribed by Josef Málek; Jindřich Nečas; Milan Pokorný; Maria E. Schonbek

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
653 KB
Volume
199
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this paper, we exclude the possibility of existence of a singular solution of the selfsimilar type proposed by Jean Leray More precisely, using a slightly stronger hypothesis we give a simpler proof to the analogous result established by J. Nečas, M. Rúžička and V. Šverák. We also discuss the possible existence of a singular solution of pseudo‐selfsimilar type.

📜 SIMILAR VOLUMES

On the number of singular points of weak
On the number of singular points of weak solutions to the Navier-Stokes equations
✍ Gregory A. Seregin 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 71 KB 👁 2 views

## Abstract We consider a suitable weak solution to the three‐dimensional Navier‐Stokes equations in the space‐time cylinder Ω × ]0, __T__[. Let Σ be the set of singular points for this solution and Σ (__t__) ≡ {(__x, t__) ∈ Σ}. For a given open subset ω ⊆ Ω and for a given moment of time __t__ ∈]0

On the Singular Set in the Navier–Stokes
On the Singular Set in the Navier–Stokes Equations
✍ Hi Jun Choe; John L. Lewis 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 168 KB

We consider suitably weak solutions (u, p) to the incompressible Navier Stokes equations and under various assumptions on u obtain estimates for the size of its singular set. One of our results improves a well known theorem of Caffarelli, Kohn, and Nirenberg.

Some global regular solutions to Navier–
Some global regular solutions to Navier–Stokes equations
✍ W. M. Zaja̧czkowski 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 246 KB 👁 1 views

## Abstract First the existence of global regular two‐dimensional solutions to Navier–Stokes equations in a bounded cylinder and for boundary slip conditions is proved. Next stability of sum of two dimensional and axially symmetric solutions is proved. Copyright © 2006 John Wiley & Sons, Ltd.

Tetrahedral finite-volume solutions to t
Tetrahedral finite-volume solutions to the Navier–Stokes equations on complex configurations
✍ N.T. Frink; S.Z. Pirzadeh 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 379 KB 👁 2 views

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the USA for solving the Euler and Navier -Stokes equations on complex aerodynamic probl