On decay of a solution of the first mixed problem for the linearized system of Navier–Stokes equations in a domain with noncompact boundary

A. K. Gushchin, V. I. Ushakov, A. F. Tedeev, and other authors have investigated how stabilization rate of solutions of mixed problems for parabolic equations of second and higher orders depends on the geometry of an unbounded domain. Here an analogous problem is considered for the linearized system of Navier–Stokes equations in a domain with noncompact boundary in three-dimensional space. Estimates are obtained for the rate of decay of a solution as $t\to\infty$, in terms of a simple geometric characteristic of the unbounded domain. These estimates coincide in form with the corresponding estimates of a solution of the first mixed problem for a parabolic equation.