Statistical study of Navier-Stokes equations, I

C. Foiaş

Rendiconti del Seminario Matematico della Università di Padova (1972)

  • Volume: 48, page 219-348
  • ISSN: 0041-8994

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Foiaş, C.. "Statistical study of Navier-Stokes equations, I." Rendiconti del Seminario Matematico della Università di Padova 48 (1972): 219-348. <http://eudml.org/doc/107456>.

@article{Foiaş1972,
author = {Foiaş, C.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {219-348},
publisher = {Seminario Matematico of the University of Padua},
title = {Statistical study of Navier-Stokes equations, I},
url = {http://eudml.org/doc/107456},
volume = {48},
year = {1972},
}

TY - JOUR
AU - Foiaş, C.
TI - Statistical study of Navier-Stokes equations, I
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1972
PB - Seminario Matematico of the University of Padua
VL - 48
SP - 219
EP - 348
LA - eng
UR - http://eudml.org/doc/107456
ER -

References

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  1. Agmon ( S.) [1] Lectures on Elliptic Boundary Value Problems (Van Nostrand), New York, 1965. Zbl0142.37401MR178246
  2. Bass ( J.) [1] Solutions turbulentes de certaines equations aux dérivées partielles, C. R. Acad. Sci. Paris, 249 (1959), 1456-1457. Zbl0086.40702MR107450
  3. [2] Sur l'existence des solutions turbulentes des équations de l'hydrodynamique, C. R. Acad. Sci. Paris, 252 (1961), 3392-3394. Zbl0126.42803MR135371
  4. Batchelor ( G.K.) [1]The Theory of homogeneous Turbulence, (Cambridge Univ. Press), Cambridge, 1967. Zbl0522.76051
  5. Bourbaki ( N.) [1]Integration. Ch. 5. Intégration des mesures. Eléments de mathématiques. (Hermann), Paris, 1967. Zbl0143.27101MR209424
  6. Cattabriga ( L.) [1]Su un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Sem. Mat. Univ. Padova, 31 (1961), 308-340. Zbl0116.18002MR138894
  7. Choquet ( G.) [1] Lectures on Analysis. Vol. II. Representation Theory. (W. A. Benjamin, Inc.). New York, 1969. Zbl0181.39602MR250012
  8. Dinculeanu ( N.) [1] Vector Measures (Pergamon Press), London, 1967. MR206190
  9. Doob ( J.L.) [1] Stochastic Processes. (Wiley), New York, 1953. Zbl0053.26802MR58896
  10. Dubreil-Jacotin ( M.L.) [1] Sur le passage des équations de Navier-Stokes aux équations de Reynolds, C. R. Acad. Sci. Paris, 244 (1957), 2887-2890. Zbl0078.08402MR94053
  11. Dunford ( N.)- Schwartz( J.T.) [1] Linear Operators - Part. I. General Theory (Inters. Publ.), New York, 1958. Zbl0084.10402MR1009162
  12. Foiaş( C.) [1] Ergodic problems in functional spaces related to Navier-Stokes equations. Proceedings Intern. Conf. Funct. Anal. and Rel. Topics. (Tokyo, April 1969), 290-304. Zbl0206.44701MR291885
  13. [2] Solutions statistiques des equations d'évolution non linéaire. C.I.M.E.Varenna, 1970. Zbl0241.35063
  14. Foiaş ( C.)- Prodi ( G.) [1] Sur le comportement global des solutions non-stationnaires des équations de Navier-Stokes en dimension 2. Ren. Sem. Mat. Univ. Padova, 39 (1967), 1-34. Zbl0176.54103MR223716
  15. Grisvard ( P.) [1]Le comportement asymptotique des valeurs propres d'un opérateur. Séminaire sur les Equations aux dérivées partielles. (Collège de France, 1971), IV, pp. 4.1-4.12. Zbl0212.15904
  16. Hille ( E.)- Phillips ( R.S.) [1] Functional Analysis and Semi-groups (Amer. Math. Soc. Coll. Publ.), New York, 1957. Zbl0078.10004MR89373
  17. Hinze ( J.O.) [1] Turbulence. An introduction and its Mechanism and Theory (McGraw-Hill, Inc.), New York, 1959. MR105962
  18. Hopf ( E.) [1] A mathematical example displaying features of turbulence. Comm. Pure Appl. Math., 1 (1948), 303-322. Zbl0031.32901MR30113
  19. [2] Uber die Anfangswertaufgabe für hydrodynamischen Grundgleichungen. Math. Nachrichten, 4 (1951), 2-13-251. Zbl0042.10604
  20. [3] Statistical hydrodynamics and functional calculus. J. Rat. Mech. Anal., 1 (1952), 87-123. Zbl0049.41704MR59119
  21. Hörmander ( L.) [1] Linear Partial differential Operators (Springer Verl.), Berlin, 1963. MR404822
  22. Hunt ( J.N.) [1] Incompressible Fluid mechanics (Wiley), New York, 1964. MR207282
  23. Ionescu Tulcea ( A.) and (C. T.) [1] On the lifting property II. journ. Math. Mech., 11 (1962), 777-795. Zbl0122.11701
  24. Jacobs ( K.) [1] Ergodic Theory (Aarhus Univ. Mat. Inst. Lect.), Aarhus, 1963. MR159922
  25. Kampé De Fériet ( J.) [1] Statistical mechanics of continuous media. Proc. Symp. Appl. Math., XIII (1962). Zbl0108.42802MR141260
  26. Kolmogorov ( A.N.)- TIHOMIROV (V. M.) [1] ε-entropy and ε-capacity of sets in functional spaces, Uspehi Mat. Nauk, 14 (1959), 3-86. Zbl0133.06703
  27. Krlyov ( N.)- BOGOLIUBOV (N. N.) [1] La théorie générale de la mesure dans son application a l'étude des systèmes dynamiques de la mécanique non linéaire. Ann. of Math., 38 (1937), 65-113. Zbl0016.08604MR1503326JFM63.1002.01
  28. Kuratowski ( C.) [1] Topologie, vol. I (Panstw. Wyd. Nauk), Warszawa, 1958. Zbl0102.37602MR90795
  29. Ladyzenskaya ( O.A.) [1] Global solution of the boundary problem for Navier-Stokes equations in two spatial dimensions. Doklady Acad. Nauk SSSR, 123 (1958), 427-429. Zbl0090.41502
  30. [2] The study of Navier-Stokes equations for stationary incompessible flows. Usp. Mat. Nauk., 14 (1959), 75-97. 
  31. [3] Mathematical Theory of viscous incompressible flows. (Gordon & Breach Sci. Publ.), New York, 1963. MR155093
  32. Landau ( L.)- Lifshitz ( E.) [1] Mécanique des fluides, Physique Théorique, t. VI. (Ed. Mir), Moscow, 1971. 
  33. Leray ( J.) [1] Etude de divers équations intégrales non-linéaire et de quelques problèmes que posent l'hydrodynamique. J. Math. Pures et Appl., 9e série, 12 (1933), 1-82. Zbl0006.16702
  34. [2] Essai sur le mouvement plan d'un liquide visqueux que limitent des parois. Journ. Math. Pures et Appl., 9e série, 13 (1934), 331-418. Zbl60.0727.01JFM60.0727.01
  35. [3] Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math., 63 (1934), 193-248. MR1555394JFM60.0726.05
  36. Lions ( J.L.) [1] Quelques méthodes de résolution des problèmes aux limites non linéaires (Dunod-Gauth. Vill.), Paris, 1969. Zbl0189.40603MR259693
  37. Lions ( J.L.)- Magenes ( E.) [1] Problèmes aux limites non homogènes et applications, vol. I (Dunod), Paris, 1968. Zbl0165.10801
  38. Lions ( J.L.)- PEETRE (J.) [1] Sur une classe d'espaces d'interpolation. Institut des Hautes Etudes Sc. Publ. Math., 19 (1964), 5-68. Zbl0148.11403MR165343
  39. Lions ( J.L.)- PRODI (G.) [1] Un théorème d'existence et unicité dans les équations de Navier-Stokes en dimension 2, C. R. Acad. Sci. Paris, 250 (1959), 3519-3521. Zbl0091.42105MR108964
  40. Loève ( M.) [1] Probability Theory. (Van Nostrand Corp. Inc.), Princeton, 1960. Zbl0095.12201MR123342
  41. Loomis ( L.H.) [1] An Introduction to Abstract Harmonic Analysis. (Van Nostrand Comp., Inc.), New York, 1953. Zbl0052.11701MR54173
  42. Malkus ( W.V.R.) [1] Similarity arguments for fully developed turbulence. Suppl. at Nuovo Cimento, 22 (1961), serie X, 376-384. 
  43. Masuda ( K.) [1] On the analyticity and the unique continuation theorem for solutions of the Navier-Stokes equation. Proc. Japan. Acad., 43 (1967), 827-832. Zbl0204.26901MR247304
  44. Monin ( A.S.)- Yaglom ( A.M.) [1] Statistical hydrodynamics. The Mechanics of turbulence. Part I (Izd. Nauka), Moscow, 1965. 
  45. [2] Statistical hydrodynamics. The Mechanics of turbulence. Part II (Izd. Nauka), Moscow, 1967. 
  46. Nelson ( E.) [1] Regular Probability measures on function space. Annals of Math., 69 (1959), 630-643. Zbl0087.13102MR105743
  47. Nihoul ( J.C.J.) [1] A kinematic theory of M.H.D. turbulent shear flow (A new approach to the Malkus theory of turbulence). Revue Roum. Math. p. et appl., 12 (1967), 1503-1514. Zbl0148.45901
  48. Obukov ( A.M.) [1] Statistical description of continuous fields. Proc. Geod. Inst. Akad. Nauk SSSR, 1954, no. 24 (151), 3-42. MR67404
  49. Prodi ( G.) [1] Un teorema di unicità per le equazioni di Navier-Stokes. Annali di Mat. pura e appl. (IV), 48 (1959), 173-182. Zbl0148.08202MR126088
  50. [2] Qualche risultato riguardo alle equazioni di Navier-Stokes nel caso bidimensionale. Rend. Sem. Mat. Univ. Padova, 30 (1960), 16-23. Zbl0098.17204MR115017
  51. [3] Teoremi ergodici per le equazioni della idrodinamica, C.I.M.E., Roma, 1960. Zbl0117.10504
  52. [4] On probability measures related to the Navier-Stokes equations in the 3-dimensional case (Air Force Res. Div. Contr. A.P.61(052)-414. Technical Note nr. 2 (1961)), Trieste, 1961. 
  53. [5] Résultats récents dans la théorie des équations de Navier Stokes. Les équations aux dérivées partielles (Colloques Intern. CNRS), Paris, 1962 '. Zbl0255.35076
  54. [6] Teoremi di tipo locale per il sistema di Navier-Stokes e stabilità delle soluzioni stazionarie. Rend. Sem. Mat. Univ. Padova, 32 (1962), 374-397. Zbl0108.28602MR189354
  55. Reynolds ( O.). [1] On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. Royal Soc. London, 186 (1894), 123-161. JFM26.0872.02
  56. Rosen ( G.) [1] Functional Integration theory for incompressible fluid turbulence, The Phys. of Fluids, 10 (1967), 2614-2619. Zbl0204.28505
  57. Riesz ( F.)- Sz.-Nagy ( B.) [1] Leçons d'analyse fonctionnelle (Gauthier-Vill.-Akad.-Kiado). Zbl0064.35404
  58. Rudin ( W.) [1] Fourier Analysis on Groups. (Inters. Publ.), New York, 1962. Zbl0107.09603MR152834
  59. Sansone ( G.) [1] Equazioni differenziali nel campo reale. Parte I. (Sc. Edizione), Bologna, 1948. Zbl0041.41903JFM67.0306.01
  60. Schlichting ( H.) [1] Boundary Layer Theory (4th edn. McGraw-Hill), New York, 1960. Zbl0096.20105MR76530
  61. Serrini ( J.) [1] Mathematical Principle of Classical Fluid Mechanics (Handbuch der Physik, Band VIII/1, Stromungs Mechanik I), Berlin, 1959. MR108116
  62. Vo-Khan ( K.) [1] Etude des fonctions quasi-stationnaires et de leurs applications aux équations différentielles opérationnelles. Bull. Soc. Math. France, suppl. au no. de Juin 1966, mémoire 6. Zbl0165.49504MR198302

Citations in EuDML Documents

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  1. M. I. Višik, A. V. Foursikov, Solutions statistiques homogènes des systèmes différentiels paraboliques et du système de Navier-Stokes
  2. Ciprian Foias, Ricardo M. S. Rosa, Roger Temam, Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations
  3. C. Foias, R. Temam, Solutions statistiques homogènes des équations de Navier-Stokes
  4. Ricardo M. S. Rosa, Some results on the Navier-Stokes equations in connection with the statistical theory of stationary turbulence

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