Existence of strong solutions and decay of turbulent solutions of Navier–Stokes flow with nonzero Dirichlet boundary data

Abstract

Recently, Leray's problem of the L2-decay of a special weak solution to the Navier–Stokes equations with nonhomogeneous boundary values was studied by the authors, exploiting properties of the approximate solutions converging to this solution. In this paper this result is generalized to the case of an arbitrary weak solution satisfying the strong energy inequality.