Solutions of the NavierStokes equations by group methods
Abstract
Using the machinery of Lie theory (groups and algebras) applied to the NavierStokes equations a number of exact solutions for the steady state are derived in (two) three dimensions. It is then shown how each of these generates an infinite number of time dependent solutions via (three) four arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.
 Publication:

IN: World Congress on System Simulation and Scientific Computation
 Pub Date:
 1983
 Bibcode:
 1983sssc....3...31B
 Keywords:

 Computational Fluid Dynamics;
 Lie Groups;
 NavierStokes Equation;
 Steady Flow;
 Algebra;
 Three Dimensional Flow;
 Time Dependence;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer