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On the homogenization principle in a time-periodic problem for the Navier–Stokes equations with rapidly oscillating mass force

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Abstract

We study the behavior of the set of time-periodic solutions of the three-dimensional system of Navier–Stokes equations in a bounded domain as the frequency of the oscillations of the right-hand side tends to infinity. It is established that the set of periodic solutions tends to the solution set of the homogenized stationary equation.

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Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    V. L. Khatskevich

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  1. V. L. Khatskevich
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Correspondence to V. L. Khatskevich.

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Original Russian Text © V. L. Khatskevich, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 5, pp. 764–777.

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Khatskevich, V.L. On the homogenization principle in a time-periodic problem for the Navier–Stokes equations with rapidly oscillating mass force. Math Notes 99, 757–768 (2016). https://doi.org/10.1134/S0001434616050138

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  • DOI: https://doi.org/10.1134/S0001434616050138

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