  Consider the unforced incompressible homogeneous Navier-Stokes equations on
the $d$-torus $\mathbb{T}^d$ where $d\geq 4$ is the space dimension. It is
shown that there exist nontrivial steady-state weak solutions $u\in
L^{2}(\mathbb{T}^d)$. The result implies the nonuniqueness of finite energy
weak solutions for the Navier-Stokes equations in dimensions $d \geq 4$. And it
also suggests that the uniqueness of forced stationary problem is likely to
fail however smooth the given force is.
