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On the Regularity of Weak Solutions to Time-Periodic Navier–Stokes Equations in Exterior Domains

Author

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  • Thomas Eiter

    (Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany)

Abstract

Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not have finite kinetic energy in general, the well-known regularity results for weak solutions to the corresponding initial-value problem cannot be transferred directly. The established regularity criterion demands a certain integrability of the purely periodic part of the velocity field or its gradient, but it does not concern the time mean of these quantities.

Suggested Citation

  • Thomas Eiter, 2022. "On the Regularity of Weak Solutions to Time-Periodic Navier–Stokes Equations in Exterior Domains," Mathematics, MDPI, vol. 11(1), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:141-:d:1017122
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