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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Finite time analyticity for the two- and three-dimensional Rayleigh-Taylor instability


Authors: C. Sulem and P.-L. Sulem
Journal: Trans. Amer. Math. Soc. 287 (1985), 127-160
MSC: Primary 76E99
DOI: https://doi.org/10.1090/S0002-9947-1985-0766210-5
MathSciNet review: 766210
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Abstract: The Rayleigh-Taylor instability refers to the dynamics of the interface between two ideal irrotational fluids of different densities superposed one over the other and in relative motion. The well-posedness of this problem is considered for two- and three-dimensional flows in the entire space and in the presence of a horizontal bottom. In the entire space, finite time analyticity of the interface is proven when the initial interface has sufficiently small gradients and is flat at infinity. In the presence of a horizontal bottom, the initial interface corrugations has also to be small initially but it is not required to vanish at infinity.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0766210-5
Keywords: Raleigh-Taylor instability, analyticity, well-posedness
Article copyright: © Copyright 1985 American Mathematical Society