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On uniqueness questions in the theory of viscous flow. (English) Zbl 0347.76016

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
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[1] Babenko, K. I., On stationary solutions of the problem of flow past a body of a viscous incompressible fluid.Math. USSR-Sb., 20 (1973), No. 1, 1–25. · Zbl 0285.76009 · doi:10.1070/SM1973v020n01ABEH001823
[2] Buck, R. C.,Advanced Calculus. McGraw-Hill Book Co., (1956), New York. · Zbl 0075.03801
[3] Chang, I-Dee &Finn, R., On the solutions of a class of equations occurring in continuum mechanics, with application to the Stokes paradox.Arch. Rat. Mech. Anal, 7 (1961), 388–401. · Zbl 0104.42401 · doi:10.1007/BF00250771
[4] Deny, J. &Lions, J. L., Les espaces du type de Beppo Levi.Ann. Inst. Fourier (Grenoble), 5 (1955), 305–370.
[5] Dolidze, D. E., A non-linear boundary value problem for unsteady motion of a viscous fluid.Prikl. Mat. Meh. (Akad. Nauk SSSR), 12 (1948), 165–180.
[6] Finn, R. &Noll, W., On the uniqueness and non-existence of Stokes flows.Arch. Rat. Mech. Anal., 1 (1957), 97–106. · Zbl 0079.12104 · doi:10.1007/BF00297998
[7] Finn, R., On the steady-state solutions of the Navier-Stokes equations.Acta Math., 3 (1961), 197–244. · Zbl 0126.42203 · doi:10.1007/BF02559590
[8] –, On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems.Arch. Rat. Mech. Anal., 19 (1965), 363–406. · Zbl 0149.44606 · doi:10.1007/BF00253485
[9] Foà, E.,L’industria. Milan, 43 (1929), 426.
[10] Ford, G. G., M. A. Thesis. University of British Columbia (1976).
[11] Ford, G. G. & Heywood, J. G. (in preparation).
[12] Fujita, H., On the existence and regularity of the steady-state solutions of the Navier-Stokes equation.J. Fac. Sci. Univ. Tokyo Sect. I. 9 (1961), 59–102. · Zbl 0111.38502
[13] Graffi, D., Sul teorema di unicità nella dinamica dei fluidi.Ann. Mat. Pura Appl., 50 (1960), 379–388. · Zbl 0102.41103 · doi:10.1007/BF02414524
[14] Heywood, J. G., On stationary solutions of the Navier-Stokes equations as limits of nonstationary solutions.Arch. Rat. Mech. Anal., 37 (1970), 48–60. · Zbl 0194.41402 · doi:10.1007/BF00249501
[15] –, The exterior nonstationary problem for the Navier-Stokes equations.Acta Math. 129 (1972), 11–34. · Zbl 0237.35074 · doi:10.1007/BF02392212
[16] –, On nonstationary Stokes flow past an obstacle.Indiana Univ. Math. J., 24 (1974), 271–284. · Zbl 0315.35074 · doi:10.1512/iumj.1974.24.24025
[17] –, On some paradoxes concerning two-dimensional Stokes flow past an obstacle.Indiana Univ. Math. J., 24 (1974), 443–450. · Zbl 0315.35075 · doi:10.1512/iumj.1974.24.24035
[18] Hope, E., Über die Anfangswertaufgabe für die Hydrodynamischen Grundgleichungen.Math. Nachr. 4 (1957), 213–231.
[19] Ito, S., The existence and the uniqueness of regular solution of non-stationary Navier-Stokes equation.J. Fac. Sci. Univ. Tokyo, Sect. I, 9 (1961), 103–140. · Zbl 0116.17905
[20] Kiselev, A. A. &Ladyzhenskaya, O. A., On the existence and uniqueness of the solution of the nonstationary problem for a viscous incompressible fluid.Izv. Akad. Nauk SSSR, 21 (1957), 655–680.
[21] Ladyzhenskaya, O. A.,The Mathematical Theory of Viscous Incompressible Flow. Second Edition. Gordon and Breach (1969), New York. · Zbl 0184.52603
[22] Lions, J. L. &Prodi, G., Un théorème d’existence et unicité dans les équations de Navier-Stokes en dimension 2.C.R. Acad. Sci. Paris, 248 (1959), 3519–3521. · Zbl 0091.42105
[23] Lions, J. L., Sur la régularité et l’unicité des solutions turbulentes des équations de Navier-Stokes. Rend. Sem. Mat. Padova 30 (1960), 16–23. · Zbl 0098.17205
[24] –,Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod (1969), Paris.
[25] Ma, C. M., Ph.D. Thesis. University of British Columbia (1975).
[26] Meyers, N. G. &Serrin, J.,”H=W”.Proc. Nat. Acad. Sci. USA, 51 (1964), 1055–1056. · Zbl 0123.30501 · doi:10.1073/pnas.51.6.1055
[27] Nečas, J.,Les méthodes directes en théorie des équations elliptiques. Masson et Cie, Editeurs, (1967), Paris.
[28] Odqvist, F. K. G.,Die Randwetaufgaben der Hydrodynamik zäher Flüssigkeiten. P. A. Norstedt and Söner (1928), Stockholm. See alsoMath. Z., 32 (1930), 329–375.
[29] Oseen, C. W.,Neuere Methoden und Ergebnisse in der Hydrodynamik. Akademische Verlagsgesellschaft M.G.H. (1927), Leipzig. · JFM 53.0773.02
[30] Prodi, G., Qualche risultato riguardo alle equazioni di Navier-Stokes nel caso bidimensionale.Rend. Sem. Mat. Univ. Padova, 30 (1960), 1–15. · Zbl 0098.17204
[31] –, Un teorema di unicità per le equazioni di Navier-Stokes.Ann. Mat. Pura Appl., 48 (1959), 173–182. · Zbl 0148.08202 · doi:10.1007/BF02410664
[32] Serrin, J.,Mathematical Principles of Classical Fluid Mechanics. Handbuch der Physik, vol. VIII/1. Springer-Verlag (1959). · Zbl 0086.20001
[33] –, The initial value problem for the Navier-Stokes equations.Nonlinear Problems. Edited by R. E. Langer. The Univ. of Wisconsin Press (1963), Madison.
[34] Shinbrot, M.,Lectures on Fluid Mechanics. Gordon and Breach (1973), New York. · Zbl 0295.76001
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