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 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.
Highlights
The Navier–Stokes system is a widely accepted model for describing the motion of viscous and incompressible fluids in the presence of convection
In this work we study a 3D non-stationary micropolar fluids system associated with Navier boundary conditions without friction for the velocity field and homogeneous Dirichlet boundary conditions for the microrotational velocity
From the mathematical point-of-view, the initial-value problem (1)–(2) with Dirichlet boundary conditions has been studied by several authors, and important results on existence of weak solutions and local strong solutions, large time asymptotic behavior, and general qualitative analysis, have been obtained
Summary
The Navier–Stokes system is a widely accepted model for describing the motion of viscous and incompressible fluids in the presence of convection. From the mathematical point-of-view, the initial-value problem (1)–(2) with Dirichlet boundary conditions has been studied by several authors, and important results on existence of weak solutions and local strong solutions, large time asymptotic behavior, and general qualitative analysis, have been obtained (see, for instance, the textbook [11]). They prove the existence of periodic solutions under assumptions that the flow domain is bounded and the external forces are periodic in time These results are extended by the same authors in [27], considering the case of non-homogeneous Navier boundary conditions for a bounded domain. In this work the author proved the existence of global-in-time weak solutions and, assuming additional regularity for the weak solutions, established some uniqueness results.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
