Why is the navier stokes equation difficult to solve??

Question

Why is the navier stokes equation difficult to solve??

Answer 1

This is Engineering.  As my boss always says, "If it were easy, everyone would be doing it."  Justifies our hourly rates!

Answer 2

Because they are a series of nonlinear differential equations.

Answer 3

The Navier-Stokes equations are a system of partial nonlinear differential equations. There is no general way to obtain families of solutions for nonlinear equations. So there can be no guarantee that a solution exists or that the system doesn't contain any singularities for a given set of initial conditions.  The nonlinearity in the Navier-Stokes equations is due to the presence of convective acceleration.

If you can come up with a proof for the existence and smoothness of solutions to the Navier Stokes equations, you would surely win a Nobel prize as wells a million dollars as this is one of seven millineum prize problems in mathematics.