Memes

The Navier Stokes equations represent the universal laws of physics that can model any fluid in the universe.

These equations have been around since almost two centuries now but we still understand very little about them. When we have a set of equations we expect the following to happen-

1. Solution should exist- One should be able to solve the equations

2. Solution should be unique- Given particular initial conditions, one should obtain an unique solution to the problem. For example if you and your friend pour water into a container in an identical way, keeping all parameters (pouring velocity, direction, geometry and dimensions of the container, etc) identical then you both should get the same flow pattern. Water in both the containers should behave in exactly the same way. If your friend gets air bubbles at a point then you should get them at the exact same point as well.

3. Solution should be smooth- A finite change in the input should produce a finite change in the output. It should not be erratic and unpredictable.

Unfortunately, Navier Stokes equations do not satisfy any of the conditions mentioned above.

https://medium.com/@ases2409/navier-stokes-equations-the-million-dollar-problem-78c01ec05d75