On properties of some integrals related to potentials for Stokes equations
Author:
P. A. Krutitskii
Journal:
Quart. Appl. Math. 65 (2007), 549569
MSC (2000):
Primary 31A10, 35Q30
Published electronically:
April 19, 2007
MathSciNet review:
2354887
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Abstract: The integrals arising from potentials for twodimensional 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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 Popov, A.N. Application of potential theory to solving the linearized NavierStokes system of equations in a twodimensional case. Trudy MIAN, 1971, t.116, pp.162180. (In Russian). MR 0364909 (51:1163)
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 Power, H. The completed double layer boundary integral equation method for twodimensional Stokes flow. IMA Journal of Applied Mathematics, 1993, v.51, pp.123145. MR 1244192 (94i:76020)
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 Krutitskii, P.A. The Dirichlet problem for the Helmholtz equation in the exterior of cuts in the plane. Comput. Math. Math. Phys., 1994, v.34, No.8/9, pp.10731090. MR 1300397 (95f:35046)
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 Vladimirov, V.S. Equations of Mathematical Physics. Nauka, Moscow, 1981. (In Russian; English translation of 1st edition: Marcel Dekker, N.Y., 1971.)
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 Gakhov, F.D. Boundary value problems. Fizmatlit, Moscow, 1963. (In Russian; English translation: Pergamon Press, Oxford; AddisonWesley, Reading, Mass., 1966.) MR 0198152 (33:6311)
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 Shilov, G.E. Mathematical Analysis. Special course. Fizmatlit, Moscow, 1960. (In Russian.)
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 Pozrikidis, C. Boundary integral and singularity method for linearized viscous flow. Cambridge University Press, Cambridge, 1992. MR 1156495 (93a:76027)
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 Varnhorn, W. The Stokes equations. Akademie Verlag, Berlin, 1994. MR 1282728 (95e:35162)
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Additional Information
P. A. Krutitskii
Affiliation:
Department of Mathematics, Faculty of Physics, Moscow State University, Moscow 119899, Russia
DOI:
http://dx.doi.org/10.1090/S0033569X07010540
PII:
S 0033569X(07)010540
Received by editor(s):
November 15, 2006
Published electronically:
April 19, 2007
Additional Notes:
The research was supported by the RFBR grants 050100050, 070100029 and the Bernoulli Center in Lausanne (Switzerland).
Article copyright:
© Copyright 2007 Brown University
