Large-time behavior of the weak solution to 3D Navier–Stokes equations

The weak solution to the Navier–Stokes equations in a bounded domain D ⊂ R 3 with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all t ≥ 0 . In a bounded domain D the solution decays exponentially fast as t → ∞ if the force term decays at a suitable rate.