Volume 17, Issue 6
An Explicit Formula for Corner Singularity Expansion of the Solutions to the Stokes Equations in a Polygon

Int. J. Numer. Anal. Mod., 17 (2020), pp. 900-928.

Published online: 2020-10

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• Abstract

We present corner singularity expansion for the solutions of the Stokes equations in an arbitrary polygon under the stress boundary condition, with explicit expression of its singular part and quantitative estimate of its regular part. In particular, there is a countably infinite set of angles such that a corner with one of these angles would give the solution precisely one additional logarithmic singularity, whose explicit expression is found.

• Keywords

Corner singularity, regularity, Stokes equation, stress boundary condition, fractional Sobolev space.

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@Article{IJNAM-17-900, author = {Li , Buyang}, title = {An Explicit Formula for Corner Singularity Expansion of the Solutions to the Stokes Equations in a Polygon}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {6}, pages = {900--928}, abstract = {

We present corner singularity expansion for the solutions of the Stokes equations in an arbitrary polygon under the stress boundary condition, with explicit expression of its singular part and quantitative estimate of its regular part. In particular, there is a countably infinite set of angles such that a corner with one of these angles would give the solution precisely one additional logarithmic singularity, whose explicit expression is found.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18357.html} }
TY - JOUR T1 - An Explicit Formula for Corner Singularity Expansion of the Solutions to the Stokes Equations in a Polygon AU - Li , Buyang JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 900 EP - 928 PY - 2020 DA - 2020/10 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18357.html KW - Corner singularity, regularity, Stokes equation, stress boundary condition, fractional Sobolev space. AB -

We present corner singularity expansion for the solutions of the Stokes equations in an arbitrary polygon under the stress boundary condition, with explicit expression of its singular part and quantitative estimate of its regular part. In particular, there is a countably infinite set of angles such that a corner with one of these angles would give the solution precisely one additional logarithmic singularity, whose explicit expression is found.

​Buyang Li. (2020). An Explicit Formula for Corner Singularity Expansion of the Solutions to the Stokes Equations in a Polygon. International Journal of Numerical Analysis and Modeling. 17 (6). 900-928. doi:
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