On the interior regularity of weak solutions of non-stationary Navier-Stokes equations on a riemannian manifold

Milan Đ. Đurić

Rendiconti del Seminario Matematico della Università di Padova (1969)

  • Volume: 42, page 267-297
  • ISSN: 0041-8994

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Đurić, Milan Đ.. "On the interior regularity of weak solutions of non-stationary Navier-Stokes equations on a riemannian manifold." Rendiconti del Seminario Matematico della Università di Padova 42 (1969): 267-297. <http://eudml.org/doc/107322>.

@article{Đurić1969,
author = {Đurić, Milan Đ.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {267-297},
publisher = {Seminario Matematico of the University of Padua},
title = {On the interior regularity of weak solutions of non-stationary Navier-Stokes equations on a riemannian manifold},
url = {http://eudml.org/doc/107322},
volume = {42},
year = {1969},
}

TY - JOUR
AU - Đurić, Milan Đ.
TI - On the interior regularity of weak solutions of non-stationary Navier-Stokes equations on a riemannian manifold
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1969
PB - Seminario Matematico of the University of Padua
VL - 42
SP - 267
EP - 297
LA - eng
UR - http://eudml.org/doc/107322
ER -

References

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  2. [2] Lichnerowicz, A.: Théorie globale des connexions et des groupes d'holonomie. Edizione Cremonese, Rome (1955). Zbl0116.39101
  3. [3] Hopf, E.: Über die Anfangswertaufgabe für die hydrodynamishen Grundleichungen. Math. Nachrichten4, 213-231 (1950-51). Zbl0042.10604MR50423
  4. [4] Kato, T. & Fujita, H.: On the nonstationary Navier-Stokes system. Rend Sem. Mat. Univ. Padova32, 243-260 (1962). Zbl0114.05002MR142928
  5. [5] Kiselev, A.A. & Ladyzhenskaia, O.A.: On existence and uniquess of the the nonstationary problem for any incompressible viscous fluid. Izv. Akad Nauk, SSSR, 21, 655-680, (1957) (in Russian). Zbl0131.41201MR100448
  6. [6] Kobayaszi, S.& Nomizu, K.: Fondations of Differential Geometry. Wiley (Interscience), New York, Vol. I, (1963). Zbl0119.37502
  7. [7] Kodaira, K.: Harmonic fields in Riemannian manifolds. Ann. Math.50, 585-665 (1946). Zbl0034.20502
  8. [8] Ladyzhenskaia, O.A.: On the classicality of generalized solutions of general non-linear non-stationary Navier-Stokes equations. Trudy Mat. Inst. Steclov4, 100-115 (1966). 
  9. [9] Ladyzhenskaia, O.A.: The Mathematical Theory of Viscous Incompressible Flow. New York, Gordon & Breach (Transl. From Russian). Zbl0121.42701
  10. [10] Leray, J.: Étude de diverses équations intégrales non linéares et de quelques problèmes que pose l'Hydrodynamique. J. Math. pures et appl., Série 9, 12, 1-82 (1933). Zbl0006.16702
  11. [11] Lions, J.L.: Sur l'existence de solution des équations de Navier-Stokes. C. R. Acad. Sci. Paris, 248, 2847-2850 (1959). Zbl0090.08203MR104930
  12. [12] Pogorzelski, W.: Étude de la solution fondamental de l'équation paraboliqueRiserche di Mat.5, 25-57 (1956). Zbl0072.10301MR79198
  13. [13] Prodi, G.: Un teorema di unicità per le equazioni di Navier-Stokes. Annali di Matematica pura ed applicata48, 173-182 (1959). Zbl0148.08202MR126088
  14. [14] Sobolev, S.L.: Some Applications of Functional Analysis in Mathematical Physics. Akad. Nauk SSSR (Siberian department), (1962) (In Russian). MR986735
  15. [15] Sobolevskii, P.E.: Non-stationary equations of viscous fluid dynamics. Dokl. Akad. Nauk, SSSR, 128, 45-48 (1959) (In Russian). Zbl0092.43104MR110895
  16. [16] Riesz, M.: L'intégrale de Riemann-Liouville et le probléme de Cauchy. Acta Math.81, 1-223 (1949). Zbl0033.27601MR30102
  17. [17] Yosida, K.: On the fundamental solution of the parabolic equation in a Riemannian space. Osaka Math. J., 5, 65-74 (1953). Zbl0052.32702MR56177
  18. [18] Yosida, K.: Functional Analysis. Berlin, Springer-Verlag (1965). Zbl0126.11504

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