𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On regularity of a weak solution to the Navier–Stokes equation with generalized impermeability boundary conditions

✍ Scribed by Jiří Neustupa; Patrick Penel

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
284 KB
Volume
66
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis

We consider the 3D Navier-Stokes equation with generalized impermeability boundary conditions. As auxiliary results, we prove the local in time existence of a strong solution ('strong' in a limited sense) and a theorem on structure. Then, taking advantage of the boundary conditions, we formulate sufficient conditions for regularity up to the boundary of a weak solution by means of requirements on one of the eigenvalues of the rate of deformation tensor. Finally, we apply these general results to the case of an axially symmetric flow with zero angular velocity.

📜 SIMILAR VOLUMES

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

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

On the regularity criterion of axisymmet
On the regularity criterion of axisymmetric weak solutions to the 3D Navier–Stokes equations
✍ Sadek Gala 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 224 KB

In this paper, we consider the regularity criterion of axisymmetric weak solutions to the Navier-Stokes equations in R 3 . Let u be an axisymmetric weak solution in R 3 × (0, T ), w = curl u, and w θ be the azimuthal component of w in the cylindrical coordinates. It is proved that u becomes a regula

Steady solutions of the Navier–Stokes eq
Steady solutions of the Navier–Stokes equations with threshold slip boundary conditions
✍ C. Le Roux; A. Tani 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 288 KB

## Abstract We establish the wellposedness of the time‐independent Navier–Stokes equations with threshold slip boundary conditions in bounded domains. The boundary condition is a generalization of Navier's slip condition and a restricted Coulomb‐type friction condition: for wall slip to occur the m

Weak imposition of boundary conditions f
Weak imposition of boundary conditions for the Navier–Stokes equations by a penalty method
✍ Atife Caglar; Anastasios Liakos 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 379 KB 👁 2 views

## Abstract We prove convergence of the finite element method for the Navier–Stokes equations in which the no‐slip condition and no‐penetration condition on the flow boundary are imposed via a penalty method. This approach has been previously studied for the Stokes problem by Liakos (Weak impositio