Rabinowitz, P. H. Existence and nonuniqueness of rectangular solutions of the Benard problem. (English) Zbl 0164.28704 Arch. Ration. Mech. Anal. 29, 32-57 (1968). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 89 Documents Keywords:fluid mechanics PDFBibTeX XMLCite \textit{P. H. Rabinowitz}, Arch. Ration. Mech. Anal. 29, 32--57 (1968; Zbl 0164.28704) Full Text: DOI References: [1] Krishnamurti, R., Finite amplitude thermal convection with changing mean temperature: The stability of hexagonal flows and the possibility of finite amplitude instability. Dissertation, UCLA, 1967. [2] Kosmieder, E.L., On convection on a uniformly heated plane. Beiträge zur Physik der Atmosphäre 39, 1–11 (1966). [3] Pearson, J.R.A., On convection cells induced by surface tension. J. Fluid Mech. 4, 489–500 (1958). · Zbl 0082.18804 · doi:10.1017/S0022112058000616 [4] Chandrasekar, S., Hydrodynamic and hydromagnetic stability. Oxford University Press 1961. [5] Malkus, W.V.R., & G. Veronis, Finite amplitude cellular convection. J. Fluid Mech. 4, 225–260 (1958). · Zbl 0082.39603 · doi:10.1017/S0022112058000410 [6] Busse, F., Das Stabilitätsverhalten der Zellularkonvection bei endlicher Amplitude. Dissertation, University of Munich, 1962. (Translation from the German by S.H. Davis, Rand Corp., Santa Monica, Calif. 1966.) [7] Segel, L.A., The structure of nonlinear cellular solutions of the Boussinesq equations. J. Fluid Mech. 21, 345–358 (1965). · Zbl 0244.76025 · doi:10.1017/S0022112065000228 [8] Chorin, A.J., Numerical study of thermal convection in a fluid layer heated from below. New York University, Courant Institute of Mathematical Sciences technical report, 1966. [9] Joseph, D.D., On the stability of the Boussinesq equations. Arch. Rational Mech. Anal. 20, 59–71 (1965). · Zbl 0136.23402 · doi:10.1007/BF00250190 [10] Velte, W., Stabilitätsverhalten und Verzweigung stationärer Lösungen der Navier-Stokesschen Gleichungen. Arch. Rational Mech. Anal. 16, 97–125 (1964). · Zbl 0131.41808 · doi:10.1007/BF00281334 [11] Velte, W., Stabilität und Verzweigung stationärer Lösungen der Navier-Stokesschen Gleichungen beim Taylorproblem. Arch. Rational Mech. Anal. 22, 1–14 (1966). · Zbl 0233.76054 · doi:10.1007/BF00281240 [12] Iudovich, V.I., Example of the generation of a secondary stationary or periodic flow when there is loss of stability of the laminar flow of a viscous incompressible fluid. J. of Applied Math. and Mechanics (translation of PMM) 29, 527–544 (1965). · Zbl 0148.22307 · doi:10.1016/0021-8928(65)90062-6 [13] Friedrichs, R.O., & J. J. Stoker, The nonlinear boundary value problem of the buckled plate. Amer. J. Math. 63, 839–888 (1941). · Zbl 0026.16301 · doi:10.2307/2371625 [14] Odeh, F., & I. Tadjbakhsh, Equilibrium states of elastic rings. To appear in J. Math. Anal. and Appl. · Zbl 0148.19505 [15] Berger, M., & P. Fife, On Von Kármán’sequations and the buckling of a thin elastic plate. Bull. A.M.S. 72, 1006–1011 (1966). · Zbl 0146.22103 · doi:10.1090/S0002-9904-1966-11620-8 [16] Wolkowisky, J., Existence of buckled states of circular plates. To appear in Comm. Pure and Appl. Math. · Zbl 0168.45206 [17] Berger, M., On von Kármán’sequations and the buckling of a thin elastic plate (I). The clamped plate, Bifurcation theory seminar notes. New York University, Courant Institute of Mathematical Sciences, 1967. [18] Kolodner, I.I., Heavy rotating string – a nonlinear eigenvalue problem. Comm. Pure and Appl. Math. 8, 395–408 (1955). · Zbl 0065.17202 · doi:10.1002/cpa.3160080307 [19] Odeh, F., Existence and bifurcation theorems for the Ginzburg-Landau equations. To appear in J. Math. Phys. [20] Ladyzhenskaya, O.A., The mathematical theory of viscous incompressible flow. New York: Gordon and Breach 1963. · Zbl 0121.42701 [21] Courant, R., & D. Hilbert, Methods of mathematical physics, V. 1. New York: Interscience 1953. [22] Kirchgässner, K., Die Instabilität der Strömung zwischen zwei rotierenden Zylindern gegenüber Taylor-Wirbeln für beliebige Spaltbreiten. Z.A.M.P. 12, 14–30 (1961). · Zbl 0101.42902 · doi:10.1007/BF01601104 [23] Karlin, S., Total positivity and applications V.I. Stanford Univ. Press, Stanford, Calif., to appear Dec. 1967. [24] Krein, M.G., & M.A. Rutman, Linear operators leaving invariant a cone in a Banach space, Translations of the A.M.S., Series 1, 10, 1962, pp. 199–325. [25] Reid, W.H., & D.L. Harris, Some further results on the Bénard problem. Phys. Fluids 1, 102–110 (1958). · Zbl 0082.39701 · doi:10.1063/1.1705871 [26] Dunford, N., & J.T. Schwartz, Linear Operators, Part I: General Theory. New York: Interscience 1958. · Zbl 0084.10402 [27] Iudovich, V.I., On the equations of steady state convection. P.M.M. 27, 295–300 (1963). [28] Rabinowitz, P.H., Periodic solutions of nonlinear hyperbolic partial differential equations. Comm. Pure and Appl. Math. 20, 145–205 (1967). · Zbl 0152.10003 · doi:10.1002/cpa.3160200105 [29] Nirenberg, L., On elliptic partial differential equations. Ann. Scuola Norm. Super. Pisa, Ser. 3, 13, 1–48 (1959). · Zbl 0088.07601 [30] Douglis, A., & L. Nirenberg, Interior estimates for elliptic systems of partial differential equations. Comm. Pure and Appl. Math. 8, 503–538 (1955). · Zbl 0066.08002 · doi:10.1002/cpa.3160080406 [31] Karlin, S., The existence of eigenvalues for integral operators. Trans. Amer. Math. Soc. 113, 1–17 (1964). · Zbl 0178.46804 · doi:10.1090/S0002-9947-1964-0169090-0 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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