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Homogeneous Statistical Solutions and Local Energy Inequality for 3D Navier-Stokes Equations

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Abstract

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.

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  1. Département de Mathématiques et Applications, École Normale Supérieure, 45, rue d’Ulm, 75230, Paris Cedex 05, France

    Arnaud Basson

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  1. Arnaud Basson
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Correspondence to Arnaud Basson.

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Communicated by P. Constantin

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Basson, A. Homogeneous Statistical Solutions and Local Energy Inequality for 3D Navier-Stokes Equations. Commun. Math. Phys. 266, 17–35 (2006). https://doi.org/10.1007/s00220-006-0009-1

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  • DOI: https://doi.org/10.1007/s00220-006-0009-1

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