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⊂R3D⊂R3 with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all t≥0t≥0. In a bounded domain DD the solution decays exponentially fast as t→∞t→∞ if the force term decays at a suitable rate.