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

Abstract

The weak solution to the Navier–Stokes equations in a bounded domain D ⊂ R[superscript 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