一般Q-张量模型与刚体相互作用的动力学
Dynamics of the general $Q$-tensor model interacting with a rigid body
AI总结：
本文研究一般Beris-Edwards Q-张量模型描述的向列相液晶与刚体相互作用问题，通过固定区域变换和附加质量算子方法建立线性化问题的极大L^p正则性，进而证明大数据的局部强适定性与小数据的全局强适定性。
摘要：
本文研究了由一般Beris-Edwards Q-张量模型描述的向列相液晶与刚体的流固相互作用问题。首先证明了该问题的总能量随时间递减。相应的数学问题是一个具有移动边界的拟线性混合阶系统。在变换到固定区域后，采用基于附加质量算子和提升论证的整体方法，在各向异性基空间中建立了线性化问题的极大L^p正则性。这为相互作用问题在大数据情形下的局部强适定性和小数据情形下的全局强适定性铺平了道路。
英文摘要：
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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