TY - JOUR
T1 - A Nonlocal Stokes System with Volume Constraints
AU - Du , Qiang
AU - Shi , Zuoqiang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 903
EP - 937
PY - 2022
DA - 2022/10
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2022-0002s
UR - https://global-sci.org/intro/article_detail/nmtma/21085.html
KW - Nonlocal Stokes system, nonlocal operators, smoothed particle hydrodynamics, incompressible flows, well-posedness, local limit.
AB - <p style="text-align: justify;">In this paper, we introduce a nonlocal model for linear steady Stokes system with physical no-slip boundary condition. We use the idea of volume constraint
to enforce the no-slip boundary condition and prove that the nonlocal model is well-posed. We also show that and the solution of the nonlocal system converges to the
solution of the original Stokes system as the nonlocality vanishes.</p>