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2007 | Vol. 59, nr 3 | 283-304
Tytuł artykułu

The interior Neumann problem for the Stokes resolvent system in a bounded domain in Rn

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The interior Neumann problem for the Stokes resolvent system is studied from the point of view of the potential theory. The existence and uniqueness results as well as boundary integral representations of the classical solution are given in the case of a bounded domain in Rn, having a compact but not connected boundary of class C1'" (0
Wydawca

Rocznik
Strony
283-304
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
  • Faculty of Mathematics and Computer Science Babes-Bolyai University 1 M. Kogalniceanu Str., 400084 Cluj-Napoca, Romania
Bibliografia
  • 1. M. ABRAMOWITZ, LA. STEGUN, Handbook of mathematical functions, Dover Publica-tions, Inc., New York 1980.
  • 2. W. BORCHERS, W. YARNHORN, On the boundedness of the Stokes semigroup in two-dimensional exterior domains, Math. Z., 213, 275-300, 1993.
  • 3. P. DEURING, The resolvent problem for the Stokes system in exterior domains: An ele-mentary approach, Math. Methods Appl. Sci., 13, 335-349, 1990.
  • 4. P. DEURING, The resolvent problem for the Stokes system in exterior domains: uniqueness and nonregularity in Holder spaces, Proc. Roy. Soc. Edinburgh, Sec. A., 122, 1-10, 1992.
  • 5. R. FARWING, H. SOHR, An approach to resolvent estimates for the Stokes equations in Lq-spaces, Lecture Notes in Mathematics, 1530, Springer-Yerlag, 97-110, 1990.
  • 6. R. FARWING, H. SOHR, Generalized resolvent estimates for the Stokes system in bounded and unbounded domains, J. Math. Soc. Japan, 46, 607-643, 1994.
  • 7. N,M. GUNTHER, Potential theory and its applications to basie problems of mathematical physics, Ungar, New York 1967.
  • 8. M. KOHR, An indireci boundary integral method for an oscillatory Stokes flow problem, Int. J. Math. Math. ScL, 47, 2961-2976, 2003.
  • 9. M. KOHR, A boundary integral method for an oscillatory Stokes flow past two bodies, [in:] Progress in Analysis, Vol. MI, Berlin, 2001, World Sci. PubL, 1215-1222, 2003.
  • 10. M. KOHR, A mixed boundary value problem for the unsteady Stokes system in a bounded domain in R71, Engineering Analysis with Boundary Elements, 29, 936-943, 2005.
  • 11. M. KOHR, The Dirichlet problems for the Stokes resolvent equations on bounded and exterior domains in Rn, Math. Nachr., 280, No. 5-6, 534-559, 2007.
  • 12. M. KOHR, I. POP, Viscous incompressible flow for Iow Reynolds numbers, WIT Press, Southampton (UK) 2004.
  • 13. R. KRESS, Linear integral equations, Springer, Berlin 1989.
  • 14. O. A. LADYZHENSKAYA, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York 1969.
  • 15. P. MAREMONTI, R. Russo, G. STARITA, On the Stokes equations: the boundary value problem, Advances in Fluid Dynamics, Quad. Mat. Aracne, Rome, 64-140, 1999.
  • 16. M. McCRACKEN, The resolvent problem for the Stokes equations of half-spaces in ip, SIAM J. Math. AnaL, 12, 201-228, 1981.
  • 17. H. POWER, L.C. WRÓBEL, Boundary integral methods in fluid mechanics, WIT Press: Computational Mechanics Publications, Southampton (UK) 1995.
  • 18. C. POZRIKIDIS, A singularity method for unsteady linearized flow, Phys. Fluids A, l, 1508-1520, 1989.
  • 19. C. POZRIKIDIS, A study of linearized oscillatory flow past particles by the boundary integral method, J. Fluid Mech., 202, 17-41, 1989.
  • 20. C. POZRIKIDIS, Boundary integral and singularity methods for linearized viscous flow, Cambridge Univ. Press, Cambridge 1992.
  • 21. V.A. SOLONNIKOY, Estimates for solutions of nonstationary Navier-Stokes eguations, J. Soviet. Math., 8, 467-529, 1977.
  • 22. G. STARITA, A. TARTAGLIONE, On the traction problem for the Stokes system, Mathematical Models and Methods in Applied Sciences, 12, 813-834, 2002.
  • 23. W. YARNHORN, Żur Numerik der Gleichungen von Navier-Stokes, Ph.D. thesis, Univer-sity of Paderborn 1985.
  • 24. W. YARNHORN, An explicit potential theory for the Stokes resolvent boundary value problems in three dimensions, Manuscripta Math., 70, 339-361, 1991.
  • 25. W. YARNHORN, The Stokes equations, Akademie Yerlag, Berlin 1994.
  • 26. W. YARNHORN, Boundary value problems and integral equations for the Stokes resolvent in bounded and exterior domains of R3, [in:] Theory of the Navier-Stokes Equations, J. G. HEYWOOD, K. MASUDA, R. RAUTMANN, Y. A. SOLONNIKOY [Eds.], World Sci. PubL, Singapore, 206-224, 1998.
  • 27. W. YARNHORN, The boundary value problems of the Stokes resolvent equations in n dimensions, Math. Nachr., 269-270, 210-230, 2004.
  • 28. W.E. WILLIAMS, A note on slow vibrations in a viscous fluid, J. Fluid Mech., 25, 589-590, 1966.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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