✦ LIBER ✦

About the Regularity of Solutions of the Nonstationary Navier-Stokes System

✍ Scribed by S. Chelkak; A. Koshelev

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 461 KB
Volume: 177
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19961770105

No coin nor oath required. For personal study only.

✦ Synopsis

The problem of existence of regular (continuous, Hiilder continuous) solutions of the nonstationary Navier-Stokes system is an important one in modern mathematical physics. It is closely connected with two main issues: the uniqueness of the solution and the possibility to apply approximate methods in numerical analysis and practical computations. Pointwise estimates of the velocity fields are essential for different numerical applications. We consider here mainly the multidimensional nonstationarity problem for finite (not necessarily small) times. In this paper we show that for small Reynold's numbers the boundedness of the velocity can be obtained and therefore the existence of unique strong solution can be proved for a certain class of external forces.

📜 SIMILAR VOLUMES

Boundary Regularity of Weak Solutions of

Boundary Regularity of Weak Solutions of the Navier–Stokes Equations

✍ Hi Jun Choe 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 437 KB

Sufficient conditions for the regularity

Sufficient conditions for the regularity of the solutions of the Navier–Stokes equations

✍ Luigi C. Berselli 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 101 KB 👁 2 views

In this paper we "nd su$cient conditions, involving only the pressure, that ensure the regularity of weak solutions to the Navier}Stokes equations. Conditions involving only the pressure were previously obtained in [7,4]. Following a remark in this last reference we improve, in particular, Kaniel's

Numerical solution of Navier-Stokes syst

Numerical solution of Navier-Stokes systems

✍ Jan Cihlář; Philippe Angot 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 187 KB 👁 1 views

In this paper the Navier-Stokes equations are discretized by semi-implicit schemes and the resulting symmetric or non-symmetric systems of linear equations are treated. A number of solvers for solving generally non-symmetric systems of linear equations are tested in order to find the optimal one.

Solution “in the large” of the nonstatio

Solution “in the large” of the nonstationary boundary value problem for the Navier-Stokes system with two space variables

✍ O. A. Ladyzhenskaia 📂 Article 📅 1959 🏛 John Wiley and Sons 🌐 English ⚖ 283 KB 👁 2 views

Existence and Regularity of a Class of W

Existence and Regularity of a Class of Weak Solutions to the Navier–Stokes Equations

✍ Cheng He 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 241 KB

We construct a class of weak solutions to the Navier᎐Stokes equations, which have second order spatial derivatives and one order time derivatives, of p power s Ž 2, r Ž .. summability for 1p F 5r4. Meanwhile, we show that u g L 0, T ; W ⍀ with 1rs q 3r2 r s 2 for 1r F 5r4. r can be relaxed not to ex

Interior regularity criterion via pressu

Interior regularity criterion via pressure on weak solutions to the Navier–Stokes equations

✍ Tomoyuki Suzuki 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 158 KB 👁 2 views

## Abstract Consider the nonstationary Navier–Stokes equations in Ω × (0, __T__), where Ω is a bounded domain in ℝ^3^. We prove interior regularity for suitable weak solutions under some condition on the pressure in the class of scaling invariance. The notion of suitable weak solutions makes it pos