Existence and nonuniqueness of rectangular solutions of the Bénard problem

Keywords

Mathematics, Complex system, Nonlinear system, Applied mathematics, Physics

References

• Linear operators leaving invariant a cone in a Banach spaceM. Г. Крейн, M. A. Rutman — 1950
• Stabilität und Verzweigung stationärer Lösungen der Navier-Stokesschen Gleichungen beim TaylorproblemWaldemar Velte — 1966
• Die Instabilität der Strömung zwischen zwei rotierenden Zylindern gegenüber Taylor-Wirbeln für beliebige SpaltbreitenKlaus Kirchgässner — 1961
• The Non-Linear Boundary Value Problem of the Buckled Plate.Kurt Friedrichs, J. J. Stoker — 1939
• On the equations of steady-state convectionM.R. Ukhovskii, V.I. Iudovich — 1963
• On the stability of the Boussinesq equationsDaniel D. Joseph — 1965
• Some Further Results on the Bénard ProblemW. H. Reid, D. L. Harris — 1958
• Interior estimates for elliptic systems of partial differential equationsAvron Douglis, Louis Nirenberg — 1955
• The existence of eigenvalues for integral operatorsSamuel Karlin — 1964
• On von kármán's equations and the buckling of a thin elastic plate, I the clamped plateMelvyn S. Berger — 1967
• 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 fluidV.I. Iudovich — 1965
• Periodic Solutions of Nonlinear Hyperbolie Partial Differential EquationsPaul H. Rabinowitz — 1967
• Equilibrium states of elastic ringsIradj G. Tadjbakhsh, Fadwa Odeh — 1967
• Existence and Bifurcation Theorems for the Ginzburg‐Landau EquationsFadwa Odeh — 1967
• On von Karman's equations and the buckling of a thin elastic plateMelvyn S. Berger, Paul C. Fife — 1966
• Existence of buckled states of circular platesJay H. Wolkowisky — 1967
• Heavy rotating string—a nonlinear eigenvalue problemI. I. Kolodner — 1955
• Stabilitätsverhalten und verzweigung stationärer Lösungen der navier-stokesschen gleichungenWaldemar Velte — 1964
• On convection cells induced by surface tensionJ. R. A. Pearson — 1958
• The structure of non-linear cellular solutions to the Boussinesq equationsLee A. Segel — 1965

Cited by

• Existence and structure of steady solutions of the Benard problem in a two dimensional quadrangular cavityJiřı́ Neustupa, Dennis A. Siginer — 2015
• The Numerical and Analytical Study of Bifurcation and Multicellular Flow Instability Due to Natural Convection Between Narrow Horizontal Isothermal Cylindrical annuli at High Rayleigh Numbers.D. B. Fant — 1987
• Bifurcation and stability problems in fluid dynamicsJung‐Ho Park — 2007
• Addendum to the paper "Two-Dimensional Infinite Prandtl Number Convection: Structure of Bifurcated Solutions, J. Nonlinear Sci., 17(3), 199-220, 2007"Tian Ma, Jung‐Ho Park, Shouhong Wang — 2007
• Fully discrete subgrid stabilized finite element method for the Darcy-Brinkman equations in Double-Diffusion convectionYunzhang Zhang, Zhoufeng Wang, Qili Tang — 2015
• On the occurrence of doubly periodic convection in a horizontal layer: PMM Vol. 37, N°1, 1973, pp.177–184G.K. Ter-Grigortants — 1973
• A general method to determine the stability of compressible flowsR. A. Guenther, I. Chang, F. Ows — 1979
• Some Mathematical and Numerical Issues in Geophysical Fluid Dynamics and Climate DynamicsJianping Li, Shouhong Wang — 2007
• On Two-Dimensional Magnetic Bénard Problem with Mixed Partial ViscosityJianfeng Cheng, Lili Du — 2015
• Bifurcation of infinite Prandtl number rotating convectionJung‐Ho Park — 2010
• Two-Dimensional Infinite Prandtl Number Convection: Structure of Bifurcated SolutionsJung‐Ho Park — 2007
• LINEAR STABILITY ANALYSIS GENERALIZED TO A THERMALLY-DRIVEN FLOWJean-Michel Cornet, Claude‐Henri Lamarque — 1999
• Error analysis of a fully discrete finite element variational multiscale method for the natural convection problemYunzhang Zhang, Yanren Hou, Jianping Zhao — 2014
• The Eckhaus criterion for convection roll solutions of the Oberbeck-Boussinesq equationsYoshiyuki Kagei, Wolf von Wahl — 1997
• Theoretical study of a Bénard Marangoni problemRosa Pardo San Gil, H. Herrero, Sergio Hoyas — 2011
• Convection in superposed fluid and porous layersFalin Chen, C. F. Chen — 1992
• Large Prandtl number behavior of the Boussinesq system of Rayleigh-Bénard convectionXiaoming Wang — 2004
• Rayleigh Bénard convection: dynamics and structure in the physical spaceTian Ma, Shouhong Wang — 2006
• Stability of bifurcating solutions by Leray-Schauder degreeD. H. Sattinger — 1971
• Construction of circle bifurcations of a two-dimensional spatially periodic flowZhi‐Min Chen, W.G. Price — 2006

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