×

Finite time analyticity for the two- and three-dimensional Rayleigh- Taylor instability. (English) Zbl 0517.76051


MSC:

76E30 Nonlinear effects in hydrodynamic stability
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, The International Series of Monographs on Physics, Clarendon Press, Oxford, 1961. · Zbl 0142.44103
[2] Garrett Birkhoff, Helmholtz and Taylor instability, Proc. Sympos. Appl. Math., Vol. XIII, American Mathematical Society, Providence, R.I., 1962, pp. 55 – 76.
[3] L. V. Ovsjannikov, To the shallow water theory foundation, Arch. Mech. (Arch. Mech. Stos.) 26 (1974), 407 – 422 (English, with Polish and Russian summaries). Papers presented at the Eleventh Symposium on Advanced Problems and Methods in Fluid Mechanics, Kamienny Potok, 1973. · Zbl 0283.76012
[4] Tadayoshi Kano and Takaaki Nishida, Sur les ondes de surface de l’eau avec une justification mathématique des équations des ondes en eau peu profonde, J. Math. Kyoto Univ. 19 (1979), no. 2, 335 – 370 (French). · Zbl 0419.76013
[5] V. I. Nalimov, A priori estimates of solutions of elliptic equations in the class of analytic functions, and their applications to the Cauchy-Poisson problem, Dokl. Akad. Nauk SSSR 189 (1969), 45 – 48 (Russian). · Zbl 0204.11802
[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, The Cauchy-Poisson problem, Dinamika Splošn. Sredy Vyp. 18 Dinamika Židkost. so Svobod. Granicami (1974), 104 – 210, 254 (Russian).
[8] Hideaki Yosihara, Gravity waves on the free surface of an incompressible perfect fluid of finite depth, Publ. Res. Inst. Math. Sci. 18 (1982), no. 1, 49 – 96. · Zbl 0493.76018 · doi:10.2977/prims/1195184016
[9] Bui An Ton, On a free boundary problem for an inviscid incompressible fluid, Nonlinear Anal. 6 (1982), no. 4, 335 – 347. · Zbl 0502.76027 · doi:10.1016/0362-546X(82)90020-7
[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, Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability, Comm. Math. Phys. 80 (1981), no. 4, 485 – 516. · Zbl 0476.76032
[13] Takaaki Nishida, A note on a theorem of Nirenberg, J. Differential Geom. 12 (1977), no. 4, 629 – 633 (1978). · Zbl 0368.35007
[14] M. S. Baouendi and C. Goulaouic, Remarks on the abstract form of nonlinear Cauchy-Kovalevsky theorems, Comm. Partial Differential Equations 2 (1977), no. 11, 1151 – 1162. · Zbl 0391.35006 · doi:10.1080/03605307708820057
[15] L. Nirenberg, J. Differential Geom. 6 (1972), 561-576.
[16] W. Wolibner, Un theorème sur l’existence du mouvement plan d’un fluide parfait, homogène, incompressible, pendant un temps infiniment long, Math. Z. 37 (1933), no. 1, 698 – 726 (French). · doi:10.1007/BF01474610
[17] Tosio Kato, On classical solutions of the two-dimensional nonstationary Euler equation, Arch. Rational Mech. Anal. 25 (1967), 188 – 200. · Zbl 0166.45302 · doi:10.1007/BF00251588
[18] C. Bardos and S. Benachour, Domaine d’analycité des solutions de l’équation d’Euler dans un ouvert de \?\(^{n}\), Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), no. 4, 647 – 687 (French). · Zbl 0366.35022
[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] Gregory R. Baker, Daniel I. Meiron, and Steven A. Orszag, Generalized vortex methods for free-surface flow problems, J. Fluid Mech. 123 (1982), 477 – 501. · Zbl 0507.76028 · doi:10.1017/S0022112082003164
[22] G. B. Whitham, Linear and nonlinear waves, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. · Zbl 0373.76001
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.