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On the existence of solitary waves in rotating fluids

Published online by Cambridge University Press:  14 November 2011

S. M. Sun
S. M. Sun
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A
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Extract

This paper considers the existence of axisymmetric solitary waves in an inviscid and incompressible rotating fluid bounded by a rigid cylinder. It has been obtained by many experiments and formal derivations that this flow has internal solitary waves in the fluid when equilibrium state at infinity satisfies certain conditions. This paper gives a rigorous proof of the existence of solitary wave solutions for the exact equations governing the flow under such conditions at infinity, and shows that the first-order approximations of the solitary wave solutions for the exact equations are solitary wave solutions derived formally using long-wave approximation. The ideas in the proof of the existence of solitary waves in two-dimensional stratified fluids are used and a main difficulty from the singularity at axis of rotation is overcome.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 5 , 1995 , pp. 1105 - 1129
Copyright
Copyright © Royal Society of Edinburgh 1995

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