Most of the Millennium Problems ore not mathemmatical phisics. 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

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