Exact Solutions to the Navier-Stokes Equations

Question

There are a number of exact solutions to the Navier-Stokes equations. How many exact solutions are currently known? Is it possible to enumerate all of the solutions to the Navier-Stokes equations?

Answer 1

Frank White's Viscous Fluid Flow book contains a good list of these "exact" solutions. I am not sure if it is complete though. I've provided links to a few of the solutions.

1. Steady flow between a fixed and moving plate
2. Axially moving concentric cylinders
3. Flow between rotating concentric cylinders
4. Hagan-Poiseuille flow
5. Combined Couette-Poiseuille flow between plates
6. Noncircular ducts -- fully developed flow
7. Starting flow in a circular pipe
8. Pipe flow due to an oscillating pressure gradient
9. Suddenly accelerating plate
10. Oscillating plate/oscillating freestream
11. Steady Couette flow where the moving wall suddenly stops
12. Unsteady Couette flow between a fixed and an oscillating plate
13. Radial outflow from a porous cylinder
14. Radial outflow between two circular plates
15. Combined Poiseuille and Couette flow in a tube or annulus
16. Gravity-driven thin fluid films
17. Decay of a line Oseen-Lamb vortex
18. The Taylor vortex profile
19. Uniform suction on a plane
20. Flow between plates with bottom injection and top suction
21. Start up of wind driven surface water
22. The Ekman Spiral
23. Plane stagnation flow
24. Axisymmetric stagnation flow
25. Flow near an infinite rotating disk
26. Jeffrey-Hamel flow in a wedge-shaped region
27. Stokes' Solution for an Immersed Sphere -- Creeping Flow
28. Creeping flow past a fluid sphere
29. Blasius boundary layer
30. Falkner-Skan-Cooke boundary layer
31. Compressible self-similar boundary layer
32. Free-shear flows
33. Plane laminar wake -- far field
34. Plane laminar jet
35. Flat-plate with uniform wall-suction