CC BY 4.0 UnportedEiter, Thomas2023-04-042023-04-042022https://oa.tib.eu/renate/handle/123456789/11918http://dx.doi.org/10.34657/10951Consider 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.enghttps://creativecommons.org/licenses/by/4.0510exterior domainOseen problemregularity criterionSerrin conditiontime-periodic solutionsweak solutionsArticle