WIAS Preprint No. 2979, (2022)

On the regularity of weak solutions to time-periodic Navier--Stokes equations in exterior domains


  • Eiter, Thomas
    ORCID: 0000-0002-7807-1349

2020 Mathematics Subject Classification

  • 35B10 35B65 35Q30 76D03 76D05 76D07


  • Time-periodic solutions, weak solutions, exterior domain, regularity criterion, Serrin condition, Oseen problem




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.

Appeared in

  • Mathematics, 11 (2023), pp. 141/1--141/17 (published online on 27.12.2022), DOI 10.3390/math11010141 .

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