Most of the Millennium Problems ore not mathematical physics.  But one or two are.  You want specific?  Here you go:
>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.

[source][1]


  [1]: https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness