[drkevorkian]

Two counterpoints:

1) What you've written, where H is independent of t is reducible to just the Eigenvalue problem for H. Certainly better understood than fluid dynamics. Even with time-dependent hamiltonians we have decent tools for talking about the solutions (Dyson series).

2) Of course for certain values of H, (esp. in continuous space) you can contrive ways of making the eigenvalue problem hard, but you don't have to go as far as quantum mechanics to find difficulty. Just take three bodies under newton's gravitation.

Yes, the quantum n-body problem is exponentially harder in n, but that's a fundamentally different type of "hardness" than the hardness of Navier-Stokes.

[Xcelerate]

1) is reducible to just the Eigenvalue problem for H. Certainly better understood than fluid dynamics.

I feel like that's akin to stating that Fermat's theorem just shows there is no n > 2 such that x^n + y^n = z^n

2) you can contrive ways of making the eigenvalue problem hard

You've got this backward. You can contrive ways of making it easy. Almost all physical problems for any system larger than but the simplest of atoms is incredibly hard.