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Volume 15, Issue 4
A Nonlocal Stokes System with Volume Constraints

Qiang Du & Zuoqiang Shi

DOI: 10.4208/nmtma.OA-2022-0002s

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 903-937.

Published online: 2022-10

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  • Abstract

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.

  • Keywords

Nonlocal Stokes system, nonlocal operators, smoothed particle hydrodynamics, incompressible flows, well-posedness, local limit.

  • AMS Subject Headings

45P05, 45A05, 35A23, 46E35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-15-903, author = {Du , Qiang and Shi , Zuoqiang}, title = {A Nonlocal Stokes System with Volume Constraints}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {4}, pages = {903--937}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0002s}, url = {http://global-sci.org/intro/article_detail/nmtma/21085.html} }
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 -

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.

Qiang Du & Zuoqiang Shi. (2022). A Nonlocal Stokes System with Volume Constraints. Numerical Mathematics: Theory, Methods and Applications. 15 (4). 903-937. doi:10.4208/nmtma.OA-2022-0002s
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