Group-theoretic analysis of the Navier-Stokes equations in the rotationally symmetric case and some new exact solutions

1983 ◽  
Vol 21 (3) ◽  
pp. 314-327 ◽  
Author(s):  
L. V. Kapitanskii
Keyword(s):  
Exact Solutions ◽  
Stokes Equations ◽  
Symmetric Case ◽  
Navier Stokes ◽  
Theoretic Analysis ◽  
Navier Stokes Equations ◽  
New Exact Solutions ◽  
Rotationally Symmetric

New Exact Axisymmetric Solutions to the Navier–Stokes Equations

2019 ◽  
Vol 75 (1) ◽  
pp. 29-42
Author(s):  
Oleg Bogoyavlenskij
Keyword(s):  
Exact Solutions ◽  
Stokes Equations ◽  
Dimensional Space ◽  
Phase Portraits ◽  
Navier Stokes ◽  
Elementary Functions ◽  
Navier Stokes Equations ◽  
New Exact Solutions ◽  
Whole Space ◽  
Dependent Viscosity

AbstractInfinite-dimensional space of axisymmetric exact solutions to the Navier–Stokes equations with time-dependent viscosity $\nu(t)$ is constructed. Inner transformations of the exact solutions are defined that produce an infinite sequence of new solutions from each known one. The solutions are analytic in the whole space ℝ3 and are described by elementary functions. The bifurcations of the instantaneous (for $t={t_{0}}$) phase portraits of the viscous fluid flows are studied for the new exact solutions. Backlund transforms between the axisymmetric Helmholtz equation and a linear case of the Grad–Shafranov equation are derived.

Some new exact solutions for the two-dimensional Navier–Stokes equations

2007 ◽  
Vol 371 (5-6) ◽  
pp. 438-452 ◽  
Author(s):  
Chiping Wu ◽  
Zhongzhen Ji ◽  
Yongxing Zhang ◽  
Jianzhong Hao ◽  
Xuan Jin
Keyword(s):  
Exact Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
New Exact Solutions

On the Generalized Navier-Stokes Equations

2003 ◽  
Author(s):  
Moustafa El-Shahed ◽  
Ahmed Salem
Keyword(s):  
Exact Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hankel Transforms ◽  
Fourier Sine ◽  
Special Cases

In this paper, we present a general Inodel of the classical Navier-Stokes equations. With the help of Laplace, Fourier Sine transforms, finite Fourier Sine transforms, and finite Hankel transforms, an exact solutions for three different special cases have been obtained.

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