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Spatially homogeneous solutions of 3D stochastic Navier-Stokes equations and local energy inequality

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  • Basson, Arnaud

Abstract

We study the three-dimensional stochastic Navier-Stokes equations with additive white noise, in the context of spatially homogeneous solutions in , i.e. solutions with a law invariant under space translations. We prove the existence of such a solution, with the additional property of being suitable in the sense of Caffarelli, Kohn and Nirenberg: it satisfies a localized version of the energy inequality.

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  • Basson, Arnaud, 2008. "Spatially homogeneous solutions of 3D stochastic Navier-Stokes equations and local energy inequality," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 417-451, March.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:3:p:417-451
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    References listed on IDEAS

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    1. Peszat, Szymon & Zabczyk, Jerzy, 1997. "Stochastic evolution equations with a spatially homogeneous Wiener process," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 187-204, December.
    2. Dawson, Donald A. & Salehi, Habib, 1980. "Spatially homogeneous random evolutions," Journal of Multivariate Analysis, Elsevier, vol. 10(2), pages 141-180, June.
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