
Accession Number : ADA306714
Title : Existence of Solitary Internal Waves in a TwoLayer Fluid of Infinite Height,
Corporate Author : VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF MATHEMATICS
Personal Author(s) : Sun, S. M.
PDF Url : ADA306714
Report Date : 27 SEP 1995
Pagination or Media Count : 32
Abstract : This paper concerns the existence of internal solitary waves moving with a constant speed at the interface of a twolayer fluid with infinite height. The fluids are immiscible, inviscid, and incompressible with constant but different densities. Assume that the height of the upper fluid is infinite and the depth of the lower fluid is finite. It has been formally derived before that under longwave assumption the firstorder approximation of the interface satisfies the BenjaminOno equation, which has algebraic solitarywave solutions. This paper gives a rigorous proof of the existence of solitarywave solutions of the exact equations governing the fluid motion, whose firstorder approximations are the algebraic solitarywave solutions of the BenjaminOno equation. The proof relies on estimates of integral operators using Fourier transforms in L2(R) space and is different from the previous existence proof of solitary waves in a twolayer fluid with finite depth.
Descriptors : *INVISCID FLOW, *TWO PHASE FLOW, *INTERNAL WAVES, MATHEMATICAL MODELS, FOURIER TRANSFORMATION, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, PARTIAL DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, NONLINEAR ALGEBRAIC EQUATIONS, INCOMPRESSIBLE FLOW, STEADY FLOW, BERNOULLI DISTRIBUTION, BANACH SPACE.
Subject Categories : Fluid Mechanics
Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE