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.

中文翻译：

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具有纳维滑移边界条件的 3D 非平稳微极流体方程

微极流体是具有微观结构的流体，属于一类具有非对称应力张量的流体，称为极地流体，作为特例，包括完善的 Navier-Stokes 模型。在这项工作中，我们研究了 3D 微极流体模型，该模型具有 Navier 边界条件，速度场无摩擦，角速度均匀 Dirichlet 边界条件。使用伽辽金方法，我们证明了弱解的存在性，并建立了 Prodi-Serrin 正则类型的结果，使我们能够在有限时间内获得全局时间强解。