论文标题
在活性液晶中固定压缩流的方程方程的弱解
Weak solutions to the equations of stationary compressible flows in active liquid crystals
论文作者
论文摘要
在有界的三维结构域中考虑了活性液晶的固定压缩流的方程。该系统由固定的Navier-Stokes方程组成，并与Q量的方程式和活动粒子的方程组成。通过两级近似方案，紧凑性估计和弱收敛参数建立了固定问题的弱解决方案的存在。开发了新的技术来克服由于固定溶液的规律性较低而引起的困难，Moser型迭代被用来处理活性颗粒和流体的强耦合，并且对能量函数的一些加权估计值可以实现，以便可以为弱解决方案构建，以便为绝对型号$γ>γ> 1 $ $γ> $ 1 $ 1 $构建。
The equations of stationary compressible flows of active liquid crystals are considered in a bounded three-dimensional domain. The system consists of the stationary Navier-Stokes equations coupled with the equation of Q-tensors and the equation of the active particles. The existence of weak solutions to the stationary problem is established through a two-level approximation scheme, compactness estimates and weak convergence arguments. Novel techniques are developed to overcome the difficulties due to the lower regularity of stationary solutions, a Moser-type iteration is used to deal with the strong coupling of active particles and fluids, and some weighted estimates on the energy functions are achieved so that the weak solutions can be constructed for all values of the adiabatic exponent $γ>1$.
