Yudovich, V. I. Cosymmetry, degeneration of solutions of operator equations, and origin of a filtration convection. (English. Russian original) Zbl 0747.47010 Math. Notes 49, No. 5, 540-545 (1991); translation from Mat. Zametki 49, No. 5, 142-148 (1991). The cosymmetry and degeneration properties of solutions of operator equations, origin of filtration convection is investigated. There is proved that noncosymmetric solutions in general creates oneparametric systems. The Euler bifurcation of the trivial cosymmetric solution of the equation with real parameter and related oneparametric system is also investigated. Reviewer: J.Vaníček (Praha) Cited in 3 ReviewsCited in 15 Documents MSC: 47A50 Equations and inequalities involving linear operators, with vector unknowns 76A02 Foundations of fluid mechanics Keywords:cosymmetry; degeneration properties of solutions of operator equations; filtration convection; oneparametric systems; Euler bifurcation PDF BibTeX XML Cite \textit{V. I. Yudovich}, Math. Notes 49, No. 5, 540--545 (1991; Zbl 0747.47010); translation from Mat. Zametki 49, No. 5, 142--148 (1991) Full Text: DOI OpenURL References: [1] D. V. Lyubimov, ?On convective motions in a porous medium, being heated from below,? Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 131-137 (1975). [2] L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978). · Zbl 0484.58001 [3] P. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, Berlin-New York (1986). · Zbl 0588.22001 [4] M. M. Vainberg and V. A. Trenogin, Branching Theory of Solutions of Nonlinear Equations [in Russian], Nauka, Moscow (1972). · Zbl 0274.47033 [5] M. A. Krasnosel’skii, Topological Methods in the Theory of Nonlinear Integral Equations [in Russian], Gosudarstvennoe Izdatel’stvo Tekhnikoteoreticheskoi Literatury, Moscow (1956). [6] Y. Katto and T. Masuoka, ?Criterion for the onset of convective flow in a fluid in a porous medium,? Int. J. Heat Mass Transfer,10, No. 3, 297-309 (1967). [7] V. I. Yudovich, The Linearization Method in the Hydrodynamic Theory of Stability [in Russian], Izdatel’stvo Rostov. Gos. Universiteta, Rostov-on-Don (1984). · Zbl 0553.76038 [8] V. S. Sorokin, ?On the stationary motions in a fluid, heated from below,? Prikl. Mat. Mekh.,18, No. 2, 197-204 (1954). · Zbl 0058.19701 [9] V. I. Yudovich, ?Free convection and branching,? Prikl. Mat. Mekh.,31, No. 1, 101-111 (1967). · Zbl 0173.28803 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.