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Zeitschrift für Analysis und ihre Anwendungen


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Volume 6, Issue 3, 1987, pp. 257–279
DOI: 10.4171/ZAA/248

Published online: 1987-06-30

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

Bernd Krause

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.

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Krause Bernd: Translationshomogene statistische Lösungen dér Navier–Stokesschen Gleichungen in einem dreidimensionalen Kanalgebiet. Z. Anal. Anwend. 6 (1987), 257-279. doi: 10.4171/ZAA/248