Abstract.
A compressible Stokes system is studied in a polygon with one concave vertex. A corner singularity expansion is obtained up to second order. The expansion contains the usual corner singularity functions for the velocity plus an “associated” velocity singular function, and a pressure singular function. In particular the singularity of pressure is not local but occurs along the streamline emanating from the incoming concave vertex. It is observed that certain first derivatives of the pressure become infinite along the streamline of the ambient flow emanating from the concave vertex. Higher order regularity is shown for the remainder.
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Communicated by H. Beirão da Veiga
This work was supported by the Com2MaC-SRC/ERC program of MOST/KOSEF (grant R11-1999-054), and by the U.S. National Science Foundation.
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Kweon, J.R., Kellogg, R.B. The Pressure Singularity for Compressible Stokes Flows in a Concave Polygon. J. math. fluid mech. 11, 1–21 (2009). https://doi.org/10.1007/s00021-007-0245-y
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DOI: https://doi.org/10.1007/s00021-007-0245-y