Compare with fluid dynamics; it's not hard to write down the Navier–Stokes equations, but there's a million dollars available to the first person who can prove or give a counter-example of the following statement:
In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.
- https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_sm...