Abstract
One considers the problem of unsteady motion of a layer of an ideal incompressible fluid with a free boundary under the presence of Taylor instability. One proves a theorem on the nonexistence of solutions In the class of initial data possessing a finite smoothness.
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Literature cited
G. Taylor, “The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I,” Proc. R. Soc. London Ser. A,201, A, 192–196 (1950).
G. Birkhoff, “Helmholtz and Taylor instability,” In: Proc. Symp. Appl. Math., Vol. 11, Am. Math. Soc., Providence (1962), pp. 116–126.
K. I. Babenko and V. Yu. Petrovich, “On the Rayleigh-Taylor instability,” Dokl. Akad. Nauk SSSR,245, No. 3, 551–553 (1979).
V. M. Goloviznin, A. A. Samarskii, and A. G. Favorskii, “A variational approach for the construction of finite-difference mathematical models in hydrodynamics,” Dokl. Akad. Nauk SSSR,235, No. 6, 1285–1288 (1977).
L. V. Ovsyannikov, “General equations and examples,” In: The Problem of the Unsteady Motion, of a Fluid with a Free Boundary [in Russian], Novosibirsk (1967), pp. 5–75.
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Qualilinear Elliptic Equations, Academic Press, New York (1968).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 96, pp. 240–246, 1980.
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Plotnikov, P.I. Ill-posedness of the nonlinear problem of the development of Taylor instability. J Math Sci 21, 824–829 (1983). https://doi.org/10.1007/BF01094445
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DOI: https://doi.org/10.1007/BF01094445