TY - JOUR
T1 - Weak solutions to the equations of stationary compressible flows in active liquid crystals
AU - Liang, Zhilei
AU - Majumdar, Apala
AU - Wang, Dehua
AU - Wang, Yixuan
N1 - This has been accepted for publication in the 'Communications in Mathematical Analysis and Applications'.
PY - 2023/3/30
Y1 - 2023/3/30
N2 - 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 $\gamma>1$.
AB - 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 $\gamma>1$.
KW - active liquid crystals
KW - stationary compressible flows
KW - Navier-Stokes equations
KW - Q-tensor
KW - weak solutions
KW - weak convergence
U2 - 10.48550/arXiv.2205.00358
DO - 10.48550/arXiv.2205.00358
M3 - Article
SN - 2790-1920
VL - 2023
SP - 70
EP - 114
JO - Communications in Mathematical Analysis and Applications
JF - Communications in Mathematical Analysis and Applications
IS - 2
ER -