Of the first mixed problem for the system of Navier–Stokes equations in domains with noncompact boundaries

This article contains an investigation of the behavior as $t\to\infty$ of a solution of the mixed problem with Dirichlet conditions on the boundary for the system of Navier–Stokes equations in an unbounded three-dimensional domain. An estimate, determined by the geometry of the domain, is proved for the rate of decay of a solution for a compactly supported initial function satisfying a certain smallness condition. This estimate coincides in form with the sharp estimate obtained earlier by the author for the solution of the first mixed problem for the heat equation.