scholarly journals A survey of geometric constraints on the blowup of solutions of the Navier–Stokes equation

Author(s):  
Evan Miller
1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin

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.


1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar

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.


2013 ◽  
Vol 291-294 ◽  
pp. 1981-1984
Author(s):  
Zhang Xia Guo ◽  
Yu Tian Pan ◽  
Yong Cun Wang ◽  
Hai Yan Zhang

Gunpowder was released in an instant when the pill fly out of the shell during the firing, and then formed a complicated flow fields about the muzzle when the gas expanded sharply. Using the 2 d axisymmetric Navier-Stokes equation combined with single equation turbulent model to conduct the numerical simulation of the process of gunpowder gass evacuating out of the shell without muzzle regardless of the pill’s movement. The numerical simulation result was identical with the experimental. Then simulated the evacuating process of gunpowder gass of an artillery with muzzle brake. The result showed complicated wave structure of the flow fields with the muzzle brake and analysed the influence of muzzle brake to the gass flow field distribution.


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