On the integral representation of the solution to the Stokes system
Valli, Alberto
Rendiconti del Seminario Matematico della Università di Padova, Tome 74 (1985), p. 85-114 / Harvested from Numdam
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Publié le : 1985-01-01
@article{RSMUP_1985__74__85_0,
     author = {Valli, Alberto},
     title = {On the integral representation of the solution to the Stokes system},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {74},
     year = {1985},
     pages = {85-114},
     mrnumber = {818719},
     zbl = {0593.35066},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1985__74__85_0}
}

Valli, Alberto. On the integral representation of the solution to the Stokes system. Rendiconti del Seminario Matematico della Università di Padova, Tome 74 (1985) pp. 85-114. http://gdmltest.u-ga.fr/item/RSMUP_1985__74__85_0/

[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. | MR 162050 | Zbl 0123.28706

[2] R. Berker, Intégration des équations du mouvement d'un fluide visqueux incompressible, Handbuch der Physik, VIII/2, Springer-Verlag, Berlin Göttingen Heidelberg, 1963, pp. 1-384. | MR 161513

[3] T. Boggio, Sul moto stazionario lento di una sfera in un liquido viscoso, Rend. Circ. Mat. Palermo, 30 (1910), pp. 65-81. | JFM 41.0824.03

[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)). | MR 553920 | Zbl 0499.35022

[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. | Numdam | MR 138894 | Zbl 0116.18002

[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. | MR 249017 | Zbl 0208.26402

[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. | JFM 51.0664.04

[8] H. Faxén, Fredholmsche Integralgleichungen zu der Hydrodynamik zäher Flüssigkeiten I, Ark. Mat. Astronom. Fys., 21A (no. 14) (1928-29), pp. 1-40. | JFM 55.1127.03

[9] G.B. Folland, Introduction to partial differential equations, Princeton University Press, Princeton, 1976. | MR 599578 | Zbl 0841.35001

[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. | MR 641818 | Zbl 0492.35018

[11] A. Korn, Allgemeine Lösung des Problems kleiner, stationärer Bewegungen in reibenden Flüssigkeiten, Rend. Circ. Mat. Palermo, 25 (1908), pp. 259-271. | JFM 39.0797.01

[12] A. Korn, Sur les monvements stationnaires d'un liquide doué de frottement, C. R. Acad. Sci. Paris, 151 (1910), pp. 50-53, 352. | JFM 41.0821.02

[13] M. Krzy, Partial differential equations of second order, I, PWN-Polish Scientific Publishers, Warszawa, 1971 (translated from polish). | Zbl 0209.40003

[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)). | MR 119676 | Zbl 0127.31703

[15] O.A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, 2nd english ed., Gordon and Breach, New York London Paris, 1969 (translated from russian). | MR 254401 | Zbl 0121.42701

[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)). | MR 467031 | Zbl 0388.35061

[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. | Zbl 0006.16702

[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. | JFM 54.0905.02 | MR 1544967

[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. | JFM 27.0645.02

[20] H.A. Lorentz, Abhandlungen über theoretische Physik, I, Teubner, Leipzig-Berlin, 1906. | JFM 37.0802.01

[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). | MR 713680

[22] C. Miranda, Partial differential equations of elliptic type, 2nd revised ed., Springer-Verlag, New York Heidelberg Berlin, 1970. | MR 284700 | Zbl 0198.14101

[23] M.A. Modjtahédi, Quelques problèmes concernant le mouvement des fluides visqueux, Thèse, Paris, 1938. | JFM 65.1494.05 | Numdam

[24] F.K.G. Odqvist, Die Randwertaufgaben der Hydrodynamik zäher Flüssigkeiten, Dissertation, Stockholm, 1928. | JFM 54.0923.19

[25] F.K.G. Odqvist, Über die Randwertaufgaben der Hydrodynamik zäher Flüssigkeiten, Math. Z., 32 (1930), pp. 329-375. | JFM 56.0713.04 | MR 1545170

[26] C.W. Oseen, Über ein Randwertproblem in der Hydrodynamik, Ark. Mat. Astronom. Fys., 18 (no. 17) (1924), pp. 1-5. | JFM 51.0666.06

[27] C.W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik, Akademische Verlagsgesellschaft M.B.H., Leipzig, 1927. | JFM 53.0773.02

[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)). | MR 139855 | Zbl 0105.38904

[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)). | MR 121563 | Zbl 0097.30404

[30] R. Temam, Navier-Stokes equations. Theory and numerical analysis, North-Holland Publishing Company, Amsterdam New York Oxford, 1977. | MR 609732 | Zbl 0426.35003

[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. | Numdam | MR 753158 | Zbl 0542.35062

[32] H. Villat, Leçons sur les fluides visqueux, Gauthier-Villars, Paris, 1943.