Statistical study of Navier-Stokes equations, I
Rendiconti del Seminario Matematico della Università di Padova, Tome 48 (1972), pp. 219-348
partie suivante Statistical study of Navier-Stokes equations, II 
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     url = {https://www.numdam.org/item/RSMUP_1972__48__219_0/}
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Foiaş, C. Statistical study of Navier-Stokes equations, I. Rendiconti del Seminario Matematico della Università di Padova, Tome 48 (1972), pp. 219-348. https://www.numdam.org/item/RSMUP_1972__48__219_0/

Agmon (S.) [1] Lectures on Elliptic Boundary Value Problems (Van Nostrand), New York, 1965. | Zbl | MR

Bass (J.) [1] Solutions turbulentes de certaines equations aux dérivées partielles, C. R. Acad. Sci. Paris, 249 (1959), 1456-1457. | Zbl | MR

[2] Sur l'existence des solutions turbulentes des équations de l'hydrodynamique, C. R. Acad. Sci. Paris, 252 (1961), 3392-3394. | Zbl | MR

Batchelor (G.K.) [1]The Theory of homogeneous Turbulence, (Cambridge Univ. Press), Cambridge, 1967. | Zbl

Bourbaki (N.) [1]Integration. Ch. 5. Intégration des mesures. Eléments de mathématiques. (Hermann), Paris, 1967. | Zbl | MR

Cattabriga (L.) [1]Su un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Sem. Mat. Univ. Padova, 31 (1961), 308-340. | Zbl | MR | Numdam

Choquet (G.) [1] Lectures on Analysis. Vol. II. Representation Theory. (W. A. Benjamin, Inc.). New York, 1969. | Zbl | MR

Dinculeanu (N.) [1] Vector Measures (Pergamon Press), London, 1967. | MR

Doob (J.L.) [1] Stochastic Processes. (Wiley), New York, 1953. | Zbl | MR

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. | Zbl | MR

Dunford (N.)-Schwartz(J.T.) [1] Linear Operators - Part. I. General Theory (Inters. Publ.), New York, 1958. | Zbl | MR

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. | Zbl | MR

[2] Solutions statistiques des equations d'évolution non linéaire. C.I.M.E. Varenna, 1970. | Zbl

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. | Zbl | MR | Numdam

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. | Numdam

Hille (E.)-Phillips (R.S.) [1] Functional Analysis and Semi-groups (Amer. Math. Soc. Coll. Publ.), New York, 1957. | Zbl | MR

Hinze (J.O.) [1] Turbulence. An introduction and its Mechanism and Theory (McGraw-Hill, Inc.), New York, 1959. | MR

Hopf (E.) [1] A mathematical example displaying features of turbulence. Comm. Pure Appl. Math., 1 (1948), 303-322. | Zbl | MR

[2] Uber die Anfangswertaufgabe für hydrodynamischen Grundgleichungen. Math. Nachrichten, 4 (1951), 2-13-251. | Zbl

[3] Statistical hydrodynamics and functional calculus. J. Rat. Mech. Anal., 1 (1952), 87-123. | MR

Hörmander (L.) [1] Linear Partial differential Operators (Springer Verl.), Berlin, 1963. | MR

Hunt (J.N.) [1] Incompressible Fluid mechanics (Wiley), New York, 1964. | MR

Ionescu Tulcea (A.) and (C. T.) [1] On the lifting property II. journ. Math. Mech., 11 (1962), 777-795. | Zbl

Jacobs (K.) [1] Ergodic Theory (Aarhus Univ. Mat. Inst. Lect.), Aarhus, 1963. | MR

Kampé De Fériet (J.) [1] Statistical mechanics of continuous media. Proc. Symp. Appl. Math., XIII (1962). | Zbl | MR

Kolmogorov (A.N.)- TIHOMIROV (V. M.) [1] ε-entropy and ε-capacity of sets in functional spaces, Uspehi Mat. Nauk, 14 (1959), 3-86. | Zbl

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. | Zbl | MR | JFM

Kuratowski (C.) [1] Topologie, vol. I (Panstw. Wyd. Nauk), Warszawa, 1958. | Zbl | MR

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. | Zbl

[2] The study of Navier-Stokes equations for stationary incompessible flows. Usp. Mat. Nauk., 14 (1959), 75-97.

[3] Mathematical Theory of viscous incompressible flows. (Gordon & Breach Sci. Publ.), New York, 1963. | MR

Landau (L.)-Lifshitz (E.) [1] Mécanique des fluides, Physique Théorique, t. VI. (Ed. Mir), Moscow, 1971.

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. | Zbl | Numdam

[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. | JFM | Numdam

[3] Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math., 63 (1934), 193-248. | MR | JFM

Lions (J.L.) [1] Quelques méthodes de résolution des problèmes aux limites non linéaires (Dunod-Gauth. Vill.), Paris, 1969. | Zbl | MR

Lions (J.L.)-Magenes (E.) [1] Problèmes aux limites non homogènes et applications, vol. I (Dunod), Paris, 1968. | Zbl

Lions (J.L.)- PEETRE (J.) [1] Sur une classe d'espaces d'interpolation. Institut des Hautes Etudes Sc. Publ. Math., 19 (1964), 5-68. | Zbl | MR | Numdam

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. | Zbl | MR

Loève (M.) [1] Probability Theory. (Van Nostrand Corp. Inc.), Princeton, 1960. | Zbl | MR

Loomis (L.H.) [1] An Introduction to Abstract Harmonic Analysis. (Van Nostrand Comp., Inc.), New York, 1953. | Zbl | MR

Malkus (W.V.R.) [1] Similarity arguments for fully developed turbulence. Suppl. at Nuovo Cimento, 22 (1961), serie X, 376-384.

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. | Zbl | MR

Monin (A.S.)-Yaglom (A.M.) [1] Statistical hydrodynamics. The Mechanics of turbulence. Part I (Izd. Nauka), Moscow, 1965.

[2] Statistical hydrodynamics. The Mechanics of turbulence. Part II (Izd. Nauka), Moscow, 1967.

Nelson (E.) [1] Regular Probability measures on function space. Annals of Math., 69 (1959), 630-643. | Zbl | MR

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. | Zbl

Obukov (A.M.) [1] Statistical description of continuous fields. Proc. Geod. Inst. Akad. Nauk SSSR, 1954, no. 24 (151), 3-42. | MR

Prodi (G.) [1] Un teorema di unicità per le equazioni di Navier-Stokes. Annali di Mat. pura e appl. (IV), 48 (1959), 173-182. | Zbl | MR

[2] Qualche risultato riguardo alle equazioni di Navier-Stokes nel caso bidimensionale. Rend. Sem. Mat. Univ. Padova, 30 (1960), 16-23. | Zbl | MR | Numdam

[3] Teoremi ergodici per le equazioni della idrodinamica, C.I.M.E., Roma, 1960. | Zbl

[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.

[5] Résultats récents dans la théorie des équations de Navier Stokes. Les équations aux dérivées partielles (Colloques Intern. CNRS), Paris, 1962 '. | Zbl

[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. | Zbl | MR | Numdam

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. | JFM

Rosen (G.) [1] Functional Integration theory for incompressible fluid turbulence, The Phys. of Fluids, 10 (1967), 2614-2619. | Zbl

Riesz (F.)-Sz.-Nagy (B.) [1] Leçons d'analyse fonctionnelle (Gauthier-Vill.-Akad.-Kiado). | Zbl

Rudin (W.) [1] Fourier Analysis on Groups. (Inters. Publ.), New York, 1962. | Zbl | MR

Sansone (G.) [1] Equazioni differenziali nel campo reale. Parte I. (Sc. Edizione), Bologna, 1948. | JFM

Schlichting (H.) [1] Boundary Layer Theory (4th edn. McGraw-Hill), New York, 1960. | Zbl | MR

Serrini (J.) [1] Mathematical Principle of Classical Fluid Mechanics (Handbuch der Physik, Band VIII/1, Stromungs Mechanik I), Berlin, 1959. | MR

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. | Zbl | MR | Numdam