ON INTERNAL GRAVITY WAVES

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Published: Dec 1, 1998
DOI: https://doi.org/10.5556/j.tkjm.29.1998.4254
Keywords:
Contraction mapping principle free boundary prohlem internal gravity waves

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TIEN-YU SUN
Department of Mathematics, Chung-Yuan Christian University, Chung-Li, Taiwan 32023, Re­public of China.
KAI-HUI CHEN
Department of Mathematics, Chung-Yuan Christian University, Chung-Li, Taiwan 32023, Re­ public of China.

Abstract




We are concerned with the steady wave motions in a 2-fluid system with constant densities. This is a free boundary problem in which the lighter fluid is bounded above by a free surface and is separated from the heavier one down below by an interface. By using a contractive mapping principle type argument. a constructive proof to the existence of some of these exact periodic internal gravity waves is proveded.




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How to Cite
SUN, T.-Y., & CHEN, K.-H. (1998). ON INTERNAL GRAVITY WAVES. Tamkang Journal of Mathematics, 29(4), 249–269. https://doi.org/10.5556/j.tkjm.29.1998.4254
Issue
Vol. 29 No. 4 (1998)
Section
Papers
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References

J. T. Beale, "Water waves generated by a pressure disturbance on a steady stream," Duke Math. J., 47(1980), 297-323.

Sir Horace Lamb, Hydrodynamics, Dover Publications, New York 1945.

Willard J. Pierson, Jr. and Paul Fife, "Some nonlinear properties of long-crested periodic waves with lengths near 2.44 centimeters," J. of Geophysical Res., 66(1961), 163-179.

J. Reeder and M. Shinbrot, "On Wilton ripples, I : formal derivation of the phenomenon," Wave Motion, 3(1981), 115-135.

J. Reeder and M. Shinbrot, "On Wilton ripples, II: rigorous results," Arch. Rational Mech. Anal., 77(1981), 321-347.

M. Shinbrot, "Water waves over periodic bottoms in three dimensions," J. Inst. Maths Applies, 25(1980), 367-385.

J. J. Stoker, Water Waves, Interscience, New York, 1953.

T. Y. Sun, "Three-dimensional steady water waves generated by partially localized pressure disturbances," SIAM J. Math. Anal., 24(5)(1993), 1153-1178.