On the integral representation of the solution to the Stokes system

Alberto Valli

Rendiconti del Seminario Matematico della Università di Padova (1985)

  • Volume: 74, page 85-114
  • ISSN: 0041-8994

How to cite


Valli, Alberto. "On the integral representation of the solution to the Stokes system." Rendiconti del Seminario Matematico della Università di Padova 74 (1985): 85-114. <http://eudml.org/doc/108013>.

author = {Valli, Alberto},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {slow viscous; Green's method; integral representation of solution; linearized Navier-Stokes system},
language = {eng},
pages = {85-114},
publisher = {Seminario Matematico of the University of Padua},
title = {On the integral representation of the solution to the Stokes system},
url = {http://eudml.org/doc/108013},
volume = {74},
year = {1985},

AU - Valli, Alberto
TI - On the integral representation of the solution to the Stokes system
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1985
PB - Seminario Matematico of the University of Padua
VL - 74
SP - 85
EP - 114
LA - eng
KW - slow viscous; Green's method; integral representation of solution; linearized Navier-Stokes system
UR - http://eudml.org/doc/108013
ER -


  1. [1] S. Agmon - A. DOUGLIS - L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 17 (1964), pp. 35-92. Zbl0123.28706MR162050
  2. [2] R. Berker, Intégration des équations du mouvement d'un fluide visqueux incompressible, Handbuch der Physik, VIII/2, Springer-Verlag, BerlinGöttingenHeidelberg, 1963, pp. 1-384. MR161513
  3. [3] T. Boggio, Sul moto stazionario lento di una sfera in un liquido viscoso, Rend. Circ. Mat. Palermo, 30 (1910), pp. 65-81. Zbl41.0824.03JFM41.0824.03
  4. [4] M.E. Bogovski, Solution of the first boundary value problem for the equation of continuity of an incompressible medium, Soviet Math. Dokl., 20 (1979), pp. 1094-1098 (previously in Dokl. Akad. Nauk SSSR, 248 (1979), pp. 1037-1040 (russian)). Zbl0499.35022MR553920
  5. [5] L. Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Univ. Padova, 31 (1961), pp. 308-340. Zbl0116.18002MR138894
  6. [6] M.P. Colautti, Sui problemi variazionali di un corpo elastico incompressibile, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia, (8) 8 (1967), pp. 291-343. Zbl0208.26402MR249017
  7. [7] U. Crudeli, Metodo di risoluzione di un problema fondamentale nella teoria del moto lento stazionario dei liquidi viscosi, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., (6) 2 (1925), pp. 247-251. Zbl51.0664.04JFM51.0664.04
  8. [8] H. Faxén, Fredholmsche Integralgleichungen zu der Hydrodynamik zäher Flüssigkeiten I, Ark. Mat. Astronom. Fys., 21A (no. 14) (1928-29), pp. 1-40. JFM55.1127.03
  9. [9] G.B. Folland, Introduction to partial differential equations, Princeton University Press, Princeton, 1976. Zbl0841.35001MR599578
  10. [10] M. Giaquinta - G. MODICA, Nonlinear systems of the type of the stationary Navier-Stokes system, J. Reine Angew. Math., 330 (1982), pp. 173-214. Zbl0492.35018MR641818
  11. [11] A. Korn, Allgemeine Lösung des Problems kleiner, stationärer Bewegungen in reibenden Flüssigkeiten, Rend. Circ. Mat. Palermo, 25 (1908), pp. 259-271. Zbl39.0797.01JFM39.0797.01
  12. [12] A. Korn, Sur les monvements stationnaires d'un liquide doué de frottement, C. R. Acad. Sci. Paris, 151 (1910), pp. 50-53, 352. Zbl41.0821.02JFM41.0821.02
  13. [13] M. Krzy, Partial differential equations of second order, I, PWN-Polish Scientific Publishers, Warszawa, 1971 (translated from polish). Zbl0209.40003
  14. [14] O.A. Lady, Investigation of the Navier-Stokes equation for a stationary flow of an incompressible fluid, Amer. Math. Soc. Transl., (2) 25 (1963), pp. 173-197 (previously in Uspehi Mat. Nauk, 14 (1959), pp. 75-97 (russian)). Zbl0127.31703MR119676
  15. [15] O.A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, 2nd english ed., Gordon and Breach, New YorkLondonParis, 1969 (translated from russian). Zbl0121.42701MR254401
  16. [16] O.A. Ladyzhenskaya - V.A. Solonnikov, Some problems of vector analysis and generalized formulations of boundary-value problems for the Navier-Stokes equations, J. Soviet Math., 10 (1978), pp. 257-286 (previously in Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 59 (1976), pp. 81-116 (russian)). Zbl0388.35061MR467031
  17. [17] J. Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'Hydrodynamique, J. Math. Pures Appl., (9) 12 (1933), pp. 1-82. Zbl0006.16702
  18. [18] L. Lichtenstein, Über einige Existenzprobleme der Hydrodynamik. Dritte Abhandlung. Permanente Bewegungen einer homogenen inkompressiblen, zähen Flüssigkeit,Math. Z., 28 (1928), pp. 387-415, 752. Zbl54.0905.02MR1544967JFM54.0905.02
  19. [19] H.A. Lorentz, Ein allgemeiner Satz, die Bewegung einer reibenden Flüssigkeit betreffend, nebst einigen Anwendungen desselben, Zittingsverlag Akad. Wet. Amster., 5 (1896), pp. 168-175. JFM27.0645.02
  20. [20] H.A. Lorentz, Abhandlungen über theoretische Physik, I, Teubner, Leipzig-Berlin, 1906. Zbl37.0802.01JFM37.0802.01
  21. [21] A. Matsumura - T. Nishida, The initial boundary value problem for the equations of motion of compressible viscous and heat-conductive f luid, preprint University of Wisconsin, MRC Technical Summary Report n. 2237 (1981). MR713680
  22. [22] C. Miranda, Partial differential equations of elliptic type, 2nd revised ed., Springer-Verlag, New YorkHeidelbergBerlin, 1970. Zbl0198.14101MR284700
  23. [23] M.A. Modjtahédi, Quelques problèmes concernant le mouvement des fluides visqueux, Thèse, Paris, 1938. Zbl65.1494.05JFM65.1494.05
  24. [24] F.K.G. Odqvist, Die Randwertaufgaben der Hydrodynamik zäher Flüssigkeiten, Dissertation, Stockholm, 1928. JFM54.0923.19
  25. [25] F.K.G. Odqvist, Über die Randwertaufgaben der Hydrodynamik zäher Flüssigkeiten, Math. Z., 32 (1930), pp. 329-375. Zbl56.0713.04MR1545170JFM56.0713.04
  26. [26] C.W. Oseen, Über ein Randwertproblem in der Hydrodynamik, Ark. Mat. Astronom. Fys., 18 (no. 17) (1924), pp. 1-5. Zbl51.0666.06JFM51.0666.06
  27. [27] C.W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik, Akademische Verlagsgesellschaft M.B.H., Leipzig, 1927. Zbl53.0773.02JFM53.0773.02
  28. [28] P.E. Sobolevski, On the smoothness of generalized solutions of the Navier-Stokes equations, Soviet Math. Dokl., 1 (1967), pp. 341-343 (previously in Dokl. Akad. Nauk SSSR, 131 (1960), pp. 758-760 (russian)). Zbl0105.38904MR139855
  29. [29] V.A. Solonnikov, On estimates of Green's tensors for certain boundary problems, Soviet Math. Dokl., 1 (1960), pp. 128-131 (previously in Dokl. Akad. Nauk SSSR, 130 (1960), pp. 988-991 (russian)). Zbl0097.30404MR121563
  30. [30] R. Temam, Navier-Stokes equations. Theory and numerical analysis, North-Holland Publishing Company, AmsterdamNew YorkOxford, 1977. Zbl0426.35003MR609732
  31. [31] A. Valli, Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method, Ann. Scuola Norm. Sup. Pisa, (4) 10 (1983), pp. 607-647. Zbl0542.35062MR753158
  32. [32] H. Villat, Leçons sur les fluides visqueux, Gauthier-Villars, Paris, 1943. 

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