Internal waves in fluids with rapidly varying density
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1981)
- Volume: 8, Issue: 4, page 513-573
- ISSN: 0391-173X
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topTurner, R. E. L.. "Internal waves in fluids with rapidly varying density." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 8.4 (1981): 513-573. <http://eudml.org/doc/83868>.
@article{Turner1981,
author = {Turner, R. E. L.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {incompressible; inviscid; region between two horizontal planes; rapidly varying density; travelling waves of permanent form; two-dimensional steady; Euler equations; Long-Yih equation; variational formulation singular; regularized problem; symmetry properties},
language = {eng},
number = {4},
pages = {513-573},
publisher = {Scuola normale superiore},
title = {Internal waves in fluids with rapidly varying density},
url = {http://eudml.org/doc/83868},
volume = {8},
year = {1981},
}
TY - JOUR
AU - Turner, R. E. L.
TI - Internal waves in fluids with rapidly varying density
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1981
PB - Scuola normale superiore
VL - 8
IS - 4
SP - 513
EP - 573
LA - eng
KW - incompressible; inviscid; region between two horizontal planes; rapidly varying density; travelling waves of permanent form; two-dimensional steady; Euler equations; Long-Yih equation; variational formulation singular; regularized problem; symmetry properties
UR - http://eudml.org/doc/83868
ER -
References
top- [1] T.B. Benjamin, Internal waves of finite amplitude and permanent form, J. Fluid Mech., 25 (1966), pp. 241-270. Zbl0145.23602
- [2] G.H. Keulegan, Characteristics of internal solitary waves, J. Res. Nat. Bur. Standards, 51 (1953), pp. 133-140. Zbl0052.21601
- [3] R.R. Long, Solitary waves in one- and two-fluid systems, Tellus, 8 (1956), pp. 460-471.
- [4] A.S. Peters - J.J. Stoker, Solitary waves in liquids having non-constant density, Comm. Pure Appl. Math., 13 (1960), pp. 115-164. Zbl0090.43301MR112445
- [5] R.R. Long, Some aspects of the flow of stratified fluids. Part I : A theoretical investigation, Tellus, 5 (1953), pp. 42-57. MR57094
- [6] M.L. Dubreil-Jacotin, Sur les théorèmes d'existence relatifs aux ondes permanentes periodiques à deux dimensions dans les liquides hétérogènes, J. Math. Pures Appl. (9), 19 (1937), pp. 43-67. Zbl0016.05905JFM63.0771.03
- [7] C.-S. Yih, Exact solutions for steady two-dimensional flow of a stratified fluid, J. Fluid Mech., 9 (1960), pp. 161-174. Zbl0094.21204MR115460
- [8] A.M. Ter-Krikorov, Théorie exacte des ondes longues stationnaires dans un liquide hétérogène, J. Mécanique, 2 (1963), pp. 351-376. MR160400
- [9] K.O. Friedrichs - D.H. Hyers, The existence of solitary waves, Comm. Pure Appl. Math., 7 (1954), pp. 517-550. Zbl0057.42204MR65317
- [10] J. Bona - D. Bose - R.E.L. Turner, A global theory of steady waves in continuously stratified fluids, Math. Res. Center Tech. Rep., University of Wisconsin, to appear.
- [11] T.B. Benjamin, A unified theory of conjugate flows, Philos. Trans. Roy. Soc. London, A269 (1971), pp. 587-643. Zbl0226.76037MR446075
- [12] E. Zfidlfr, Bifurcation theory and permanent waves, in Applications of Bifurcation Theory, P. Rabinowitz ed., Academic Press, New York, 1977. MR459200
- [13] J.J. Stoker, Water Waves, Interscience Publishers, Inc., New York, 1957. Zbl0078.40805MR103672
- [14] J.B. McLeod - R.E.L. Turner, Bifurcation for non-differentiable operators with an application to elasticity, Arch. Rational Mech. Anal., 63 (1976), pp. 1-45. Zbl0356.47030MR473953
- [15] D. Gilbarg - N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren der mathematische Wissenschaften224, Springer-Verlag, Berlin, Heidelberg, New York, 1977. Zbl0361.35003MR473443
- [16] A. Ambrosetti - P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Functional Analysis, 14 (1973), pp. 349-381. Zbl0273.49063MR370183
- [17] O.A. Ladyzhenskaya - N.N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002MR244627
- [18] R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975. Zbl0314.46030MR450957
- [19] G. Polya - G. Szego, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematical Studies27, Princeton University Press, Princeton, 1950. Zbl0044.38301MR43486
- [20] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math., 12 (1959), pp. 623-727. Zbl0093.10401MR125307
- [21] R. Courant - D. Hilbert, Methods of Mathematical Physics, vol. II, Interscience Publishers, New York, 1962. Zbl0099.29504MR65391
- [22] C.J. Amick - J.F. Toland, On Solitary Water-Waves of Finite Amplitude, Arch. Rat. Mech. Anal., 76 (1981), pp. 9-95. Zbl0468.76025MR629699
- [23] G. Keady - J. Norbury, On the existence theory for irrotational water waves, Math. Proc. Cambridge Philos. Soc., 83 (1978), pp. 137-157. Zbl0393.76015MR502787
- [24] L.R. Walker, Interfacial solitary waves in a two-fluid medium, The Physics of Fluids, 16 (1973), pp. 1796-1804.
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