Translationshomogene statistische Lösungen dér Navier–Stokesschen Gleichungen in einem dreidimensionalen Kanalgebiet

Abstract

Homogeneous space-time statistical solutions of the Navier-Stokes equations in a three-dimensional channel are studied which are based on given homogeneous initial measure. The individual solution of the Navier-Stokes equations is approximated by a periodical Galerkin-ansatz which satisfies the boundary conditions at the walls of the channel. Suitable a priori estimates and an approximation of the initial measure allow the limit process and ensure the existence of homogeneous statistical solutions of the Navier-Stokes equations by Prochorov’s theorem.