We study a three-dimensional, incompressible, viscous, micropolar fluid with anisotropic microstructure on a periodic domain. Subject to a uniform microtorque, this system admits a unique nontrivial equilibrium. We prove that this equilibrium is nonlinearly unstable. Our proof relies on a nonlinear bootstrap instability argument which uses control of higher-order norms to identify the instability at the $$L^2$$ L 2 level.

中文翻译：

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受均匀微扭矩影响的各向异性微极流体：不稳定情况

我们研究了在周期性域上具有各向异性微观结构的三维、不可压缩、粘性微极流体。受均匀微扭矩的影响，该系统允许独特的非平凡平衡。我们证明这个平衡是非线性不稳定的。我们的证明依赖于非线性自举不稳定性论证，该论证使用高阶范数的控制来识别 $$L^2$$L 2 级别的不稳定性。