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A note on statistical solutions of the three-dimensional Navier-Stokes equations: the time-dependent case. (English. Abridged French version) Zbl 1186.35141
Summary: Time-dependent statistical solutions of the three-dimensional Navier-Stokes equations for incompressible fluids are considered. They are a mathematical formalization of the notion of ensemble averages in turbulence theory and form the backbone for a mathematical foundation of the theory of turbulence. The two main notions of statistical solutions, previously introduced, are revisited and a new formulation of one of them is given. An existence proof for this new formulation is given, along with a number of useful properties.

MSC:
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
76F02 Fundamentals of turbulence
76D06 Statistical solutions of Navier-Stokes and related equations
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