Finite time analyticity for the two and three dimensional Kelvin- Helmholtz instability. (English) Zbl 0476.76032


76B47 Vortex flows for incompressible inviscid fluids
76E05 Parallel shear flows in hydrodynamic stability
76E30 Nonlinear effects in hydrodynamic stability


Zbl 0107.427
Full Text: DOI


[1] Babenko, K.I., Petrovich, V.U.: Sov. Phys. Dokl.24, 161–163 (1979); Preprint No. 68, Inst. Prikl. Math. Moscou (1978)
[2] Baouendi, M.S., Goulaouic, C.: Comm. Part. Diff. Eq.2, 1151–1162 (1977) · Zbl 0391.35006
[3] Bardos, C.: J. Math. Anal. Appl.40, 769–790 (1972) · Zbl 0249.35070
[4] Birkhoff, G.: Los Alamos Scientific Laboratory Report LA-1862 (1954)
[5] Birkhoff, G.: Los Alamos Scientific Laboratory Report LA-1927 (1955)
[6] Birkhoff, G.: In: Hydrodynamics instability, p. 55–76. Proc. of Symp. Appl. Math. XIII, Ann. Math. Soc. (1962)
[7] Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability. Oxford: Clarendon Press 1961 · Zbl 0142.44103
[8] Kato, T.: Arch. Rat. Mech. Anal.25, 188–200 (1967) · Zbl 0166.45302
[9] Ladysenskaya, O.A., Uratlceva, N.N.: Linear and quasi-linear elliptic equations. Mathematics in Science and Engineering, Vol. 46. New York, London: Academic Press 1968
[10] Meiron, D.I., Baker, G.R., Orszag, S.A.: Analytic structure of vortex sheet dynamics. I. Kelvin-Helmholtz instability (to appear) (1980) · Zbl 0476.76031
[11] Moore, D.W.: Proc. Roy. Soc. London Ser. A365, 105–119 (1979) · Zbl 0404.76040
[12] Morf, R., Orszag, S.A., Meiron, D.I., Frisch, U., Meneguzzi, M.: In: Proc. of the Seventh International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics. Berlin, Heidelberg, New York: Springer (to appear) (1980)
[13] Nirenberg, L.: J. Diff. Geometry6, 561–576 (1972)
[14] Nishida, T.: J. Diff. Geometry12, 629–633 (1977)
[15] Ovsjannikov, L.V.: Dokl. Akad. Nauk SSSR200, No. 4; Sov. Math. Dokl.12, 1497–1502 (1971)
[16] Richtmyer, R., Morton, K.W.: Difference methods for initial value problems, 2nd ed. Interscience Tracts in Pure and Applied Mathematics (1967) · Zbl 0155.47502
[17] Saffman, P.G., Baker, G.R.: Ann. Rev. Fluid. Mech.II, 95–122 (1979)
[18] Wolibner, W.: Math. Z.37, 698–726 (1933) · Zbl 0008.06901
[19] Yudovich, V.I.: Zh. Vycisl. Mat. Fiz.3, 1032–1066 (1963)
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