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Keywords = Serrin condition

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17 pages, 384 KiB  
Article
On the Regularity of Weak Solutions to Time-Periodic Navier–Stokes Equations in Exterior Domains
by Thomas Eiter
Mathematics 2023, 11(1), 141; https://doi.org/10.3390/math11010141 - 27 Dec 2022
Cited by 1 | Viewed by 1855
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 [...] Read more.
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. Full article
14 pages, 325 KiB  
Article
A 3D Non-Stationary Micropolar Fluids Equations with Navier Slip Boundary Conditions
by Cristian Duarte-Leiva, Sebastián Lorca and Exequiel Mallea-Zepeda
Symmetry 2021, 13(8), 1348; https://doi.org/10.3390/sym13081348 - 26 Jul 2021
Cited by 1 | Viewed by 1848
Abstract
Micropolar fluids are fluids with microstructure and belong to a class of fluids with asymmetric stress tensor that called Polar fluids, and include, as a special case, the well-established Navier–Stokes model. In this work we study a 3D micropolar fluids model with [...] Read more.
Micropolar fluids are fluids with microstructure and belong to a class of fluids with asymmetric stress tensor that called Polar fluids, and include, as a special case, the well-established Navier–Stokes model. In this work we study a 3D micropolar fluids model with Navier boundary conditions without friction for the velocity field and homogeneous Dirichlet boundary conditions for the angular velocity. Using the Galerkin method, we prove the existence of weak solutions and establish a Prodi–Serrin regularity type result which allow us to obtain global-in-time strong solutions at finite time. Full article
(This article belongs to the Special Issue Mathematical Fluid Dynamics and Symmetry)
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