Year: 2023
Author: Zhilei Liang, Apala Majumdar, Dehua Wang, Yixuan Wang
Communications in Mathematical Analysis and Applications, Vol. 2 (2023), Iss. 1 : pp. 70–114
Abstract
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 $\gamma>1.$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmaa.2022-0021
Communications in Mathematical Analysis and Applications, Vol. 2 (2023), Iss. 1 : pp. 70–114
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 45
Keywords: Active liquid crystals stationary compressible flows Navier-Stokes equations Q-tensor weak solutions weak convergence.