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arXiv · 2501.01181

Dynamics of the general $Q$-tensor model interacting with a rigid body

Felix Brandt·Matthias Hieber·Arnab Roy
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Abstract

In this article, the fluid-rigid body interaction problem of nematic liquid crystals described by the general Beris-Edwards $Q$-tensor model is studied. It is proved first that the total energy of this problem decreases in time. The associated mathematical problem is a quasilinear mixed-order system with moving boundary. After the transformation to a fixed domain, a monolithic approach based on the added mass operator and lifting arguments is employed to establish the maximal $L^p$-regularity of the linearized problem in an anisotropic ground space. This paves the way for the local strong well-posedness for large data and global strong well-posedness for small data of the interaction problem.

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Felix Brandt, Matthias Hieber, Arnab Roy. 2025-09-18. Dynamics of the general $Q$-tensor model interacting with a rigid body. https://arxiv.org/abs/2501.01181

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