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

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

Mathematics, 2022, vol. 11, issue 1, 1-17

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.

Keywords: time-periodic solutions; weak solutions; exterior domain; regularity criterion; Serrin condition; Oseen problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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