WIAS Preprint No. 2979, (2022)
On the regularity of weak solutions to time-periodic Navier--Stokes equations in exterior domains
- Eiter, Thomas
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.
- Mathematics, 11 (2023), pp. 141/1--141/17 (published online on 27.12.2022), DOI 10.3390/math11010141 .