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Homogeneous statistical solutions and local energy inequality for 3D Navier-Stokes equations. (English) Zbl 1106.76017
Summary: We are interested in space-time spatially homogeneous statistical solutions of Navier-Stokes equations in space dimension three. We first review the construction of such solutions, and introduce convenient tools to study the pressure gradient. Then we show that given a spatially homogeneous initial measure with finite energy density, one can construct a homogeneous statistical solution concentrated on weak solutions which satisfy the local energy inequality.

MSC:
76D06 Statistical solutions of Navier-Stokes and related equations
76M35 Stochastic analysis applied to problems in fluid mechanics
35Q30 Navier-Stokes equations
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