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On the regularity of weak solutions to time-periodic Navier--Stokes equations in exterior domains
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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.
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Regularity and Decay for Navier-Slip Fluid-Structure Interaction in Exterior Domains
For the linearized fluid-rigid body system with Navier-slip friction in an exterior domain, the associated operator has maximal L^q regularity, generates a bounded analytic semigroup, and obeys L^r–L^q decay estimates.
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