TY - JOUR
T1 - Analysis and Optimal Control of a System of Hemivariational Inequalities Arising in Non-Stationary Navier-Stokes Equation with Thermal Effects
AU - Xuan , Hailing
AU - Cheng , Xiaoliang
AU - Wang , Xilu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 351
EP - 378
PY - 2024
DA - 2024/05
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2023-0124
UR - https://global-sci.org/intro/article_detail/nmtma/23104.html
KW - Non-stationary Navier-Stokes equation, hemivariational inequalities, thermal effects, optimal control, existence and uniqueness.
AB - <p style="text-align: justify;">In this paper, we primarily investigate the existence, dependence and optimal control results related to solutions for a system of hemivariational inequalities
pertaining to a non-stationary Navier-Stokes equation coupled with an evolution
equation of temperature field. The boundary conditions for both the velocity field
and temperature field incorporate the generalized Clarke gradient. The existence
and uniqueness of the weak solution are established by utilizing the Banach fixed
point theorem in conjunction with certain results pertaining to hemivariational inequalities. The finite element method is used to discretize the system of hemivariational inequalities and error bounds are derived. Ultimately, a result confirming the
existence of a solution to an optimal control problem for the system of hemivariational inequalities is elucidated.</p>