On properties of some integrals related to potentials for Stokes equations

Author:
P. A. Krutitskii

Journal:
Quart. Appl. Math. **65** (2007), 549-569

MSC (2000):
Primary 31A10, 35Q30

DOI:
https://doi.org/10.1090/S0033-569X-07-01054-0

Published electronically:
April 19, 2007

MathSciNet review:
2354887

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Abstract: The integrals arising from potentials for two-dimensional Stokes equations are explored in the case when the potentials are defined on the smooth open arc of an arbitrary shape, while the densities in the potentials belong to weighted Hölder space and may have power singularities. The properties of smoothness of these integrals and their derivatives are studied. The singularities of the derivatives of the integrals at the ends of the arcs are examined. The integrals studied in the paper being coupled with harmonic logarithmic potential yield single layer potentials for velocities in Stokes equations. Single layer potential for pressure in Stokes equations is investigated also.

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Additional Information

**P. A. Krutitskii**

Affiliation:
Department of Mathematics, Faculty of Physics, Moscow State University, Moscow 119899, Russia

DOI:
https://doi.org/10.1090/S0033-569X-07-01054-0

Received by editor(s):
November 15, 2006

Published electronically:
April 19, 2007

Additional Notes:
The research was supported by the RFBR grants 05-01-00050, 07-01-00029 and the Bernoulli Center in Lausanne (Switzerland).

Article copyright:
© Copyright 2007
Brown University