Addendum to: A Regularity Criterion for the Navier–Stokes Equation Involving Only the Middle Eigenvalue of the Strain Tensor

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

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Numerical approximations of the Navier–Stokes equation coupled with volume-conserved multi-phase-field vesicles system: Fully-decoupled, linear, unconditionally energy stable and second-order time-accurate numerical scheme

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2020.113600 ◽

2021 ◽

Vol 375 ◽

pp. 113600

Author(s):

Xiaofeng Yang

Keyword(s):

Stokes Equation ◽

Phase Field ◽

Numerical Scheme ◽

Second Order ◽

Navier Stokes ◽

Numerical Approximations ◽

Navier Stokes Equation ◽

Energy Stable ◽

Multi Phase

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A fractional model of Navier–Stokes equation arising in unsteady flow of a viscous fluid

Journal of the Association of Arab Universities for Basic and Applied Sciences ◽

10.1016/j.jaubas.2014.01.001 ◽

2015 ◽

Vol 17 (1) ◽

pp. 14-19 ◽

Cited By ~ 6

Author(s):

Devendra Kumar ◽

Jagdev Singh ◽

Sunil Kumar

Keyword(s):

Viscous Fluid ◽

Unsteady Flow ◽

Stokes Equation ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Fractional Model

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A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

Journal of Fluid Mechanics ◽

10.1017/s0022112073001606 ◽

1973 ◽

Vol 59 (2) ◽

pp. 391-396 ◽

Cited By ~ 2

Author(s):

N. C. Freeman ◽

S. Kumar

Keyword(s):

Shock Wave ◽

Reynolds Number ◽

Stokes Equation ◽

Stokes Equations ◽

Low Pressure ◽

Navier Stokes ◽

Spherically Symmetric ◽

Navier Stokes Equation ◽

Navier Stokes Equations ◽

Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

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