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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on September 29, 2009
The Quarterly Journal of Mechanics and Applied Mathematics 2009 62(4):495-523; doi:10.1093/qjmam/hbp020
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© The author 2009. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

On Uniqueness and Solvability in The Linear Problem of Ship Waves

O. V. Motygin{dagger}

( Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy prospect, 61, 199178 St. Petersburg, Russia )

P. Mciver{ddagger}

( School of Mathematics, Loughborough University, Loughborough, Leicestershire LE11 3TU )

{dagger} Corresponding author. <O.V.Motygin{at}gmail.com>

{ddagger} <P.McIver{at}lboro.ac.uk>

Received 23 December 2008. Revise 22 July 2009. Accepted 10 August 2009.


  Abstract

This work is devoted to the question of uniqueness and solvability for the linear problem of ship waves, describing the forward motion of rigid totally submerged bodies in an unbounded fluid with a free surface. The statement of the problem is discussed with some attention paid to the conditions at infinity. For the problem, Green's identity and boundary integral equations on the wetted surface of the bodies are derived; equivalence of the equations and the boundary-value problem is proved. New criteria and sufficient conditions of unique solvability are suggested. A uniqueness theorem is proved in the form of simple bounds of possible nonuniqueness parameters. Algorithms for verification of uniqueness and finding nonuniqueness examples are developed and numerical results illustrating the theoretical considerations are given.


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