论文标题
liouville定理用于当地莫雷空间中液晶流的固定和非平稳耦合系统
Liouville theorems for a stationary and non-stationary coupled system of liquid crystal flows in local Morrey spaces
论文作者
论文摘要
我们在这里考虑整个三维空间中简化的Ericksen-Leslie系统。该系统处理不可压缩的Navier-Stokes方程，并与谐波映射流相结合，该方程模拟了列液晶的动力学行为。对于固定（时间内的）情况和非平稳（时间取决于时间）的情况，使用相当一般的莫雷空间框架，我们在该耦合系统的未知数上获得了一些先验条件，以证明它们相同消失。该结果称为liouville型定理。作为双重产品，我们的定理还改善了有关经典Navier-Stokes方程的特定情况的Liouville型定理的一些众所周知的结果
We consider here the simplified Ericksen-Leslie system on the whole three-dimensional space. This system deals with the incompressible Navier-Stokes equations strongly coupled with a harmonic map flow which models the dynamical behavior for nematic liquid crystals. For both the stationary (time independing) case and the non-stationary (time depending) case, using the fairly general framework of a kind of local Morrey spaces, we obtain some a priori conditions on the unknowns of this coupled system to prove that they vanish identically. This results are known as Liouville-type theorems. As a bi-product, our theorems also improve some well-known results on Liouville-type theorems for the particular case of classical Navier-Stokes equations
