Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, Clarendon Press, Oxford, 1961. MR 0128226 (23:B1270)
  • [2] G. Birkhoff, Helmholtz and Taylor instability, Hydrodynamic Instability, Proc. Sympos. Appl. Math., vol. 13, Amer. Math. Soc., Providence, R.I., 1962, pp. 55-76. MR 0137423 (25:875)
  • [3] L. V. Ovsjanikov, Arch. Mech. (Arch. Mech. Stos.) 26 (1974), 407-422. MR 0347218 (49:11938)
  • [4] T. Kano and T. Nishida, J. Math. Tokyo Univ. 19 (1979), 335-370. MR 545714 (82d:76012)
  • [5] V. I. Nalimov, Dokl. Akad. Nauk. SSSR 189 (1969), 45-48. MR 0262645 (41:7250)
  • [6] J. C. W. Rogers, Water waves; analytic solutions, uniqueness and continuous dependence on the data, Naval Ordinance Laboratory NSWC/WOL/TR 75-43, 1975.
  • [7 V] I. Nalimov, Dinamika Splosh. Sredy 18 (1974), 104-210. MR 0609882 (58:29458)
  • [8] H. Yosihara, Publ. Res. Inst. Math. Sci. 18 (1982), 49-96. MR 660822 (83k:76017)
  • [9] Bui An Ton, Nonlinear Anal. Theor. Meth. Appl. 6 (1982), 335-347. MR 654810 (83g:35085)
  • [10] I. I. Bakenko and V. U. Petrovitch, Soviet Phys. Dokl. 24 (1969), 161-163.
  • [11] L. V. Ovsjanikov, Dokl. Akad. Nauk. SSSR 200 (1971); Soviet Math. Dokl. 12 (1971), 1497-1502.
  • [12] C. Sulem, P. L. Sulem, C. Bardos and U. Frisch, Comm. Math. Phys. 80 (1981), 485-516. MR 628507 (83d:76012)
  • [13] T. Nishida, J. Differential Geom. 12 (1977), 629-633. MR 512931 (80a:58013)
  • [14] M. S. Baouendi and C. Goulaouic, Comm. Partial Differential Equations 2 (1977), 1151-1162. MR 0481322 (58:1443)
  • [15] L. Nirenberg, J. Differential Geom. 6 (1972), 561-576.
  • [16] W. Wolibner, Math. Z. 37 (1933), 698-726. MR 1545430
  • [17] T. Kato, Arch. Rational Mech. Anal. 25 (1967), 188-200. MR 0211057 (35:1939)
  • [18] C. Bardos and S. Benachour, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), 647-687. MR 0454413 (56:12664)
  • [19] C. Sulem, C. R. Acad. Sci. Paris Ser. A 287 (1978), 623-628.
  • [20] M. Shiffer, Pacific J. Math. 7 (1957), 1187-1225; 9 (1959), 211-269.
  • [21] G. R. Baker, D. I. Meiron and S. A. Orszag, J. Fluid Mech. 123 (1982), 477-501. MR 687014 (84a:76002)
  • [22] G. B. Whitham, Linear and nonlinear waves, Interscience, New York, 1973, p. 114. MR 0483954 (58:3905)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 76E99

Retrieve articles in all journals with MSC: 76E99


Additional Information

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

American Mathematical Society