Conservation of momentum?

There's no a priori reason conservation of momentum would apply; for that matter in 0-angle-of-attack aviation it doesn't.

Maybe to put it differently, the "Newtonian" model of flight comes out of assuming CoM applies, which we know isn't universally true.

EDITING: of course it always "applies" in the sense that there is a definable system in which total momentum will be unchanged, the point being that there is no guarantee that's a system in which the plane gets lift greater than its weight

A symmetrical airfoil at zero angle of attack doesn't generate lift because it doesn't turn the fluid. A non symmetrical airfoil will generate lift even at zero AOA because air has viscosity and the lack of symmetry causes it to turn around the shape. When you bend fluid flow, COM comes into play.

If you're asking how to apply the Navier-Stokes equations: apply boundary conditions

If you're asking how to derive the Navier-Stokes equations, use continuum / conservation principles.