caa a22 4500 397499841 CHVBK 20180308164530.0 cr unu---uuuuu 161202e199511 xx s 000 0 eng 10.1093/qjmam/48.4.507 doi (NATIONALLICENCE)oxford-10.1093/qjmam/48.4.507 ON UNIQUENESS IN LINEARIZED TWO-DIMENSIONAL WATER-WAVE PROBLEMS FOR TWO SURFACE PIERCING BODIES [Elektronische Daten] [N. G. KUZNETSOV, M. J. SIMON] In the study of linearized water waves interacting with obstacles, the question of the uniqueness of the solution is not yet fully answered. That is, are there non-radiating (and therefore persistent) oscillatory modes at any frequency for some geometry? John (1) established uniqueness for the case where the body is surface-piercing and has the property that vertical lines from the free surface do not intersect the body. More recently, Simon and Ursell (2) generalized John's approach to prove uniqueness for a wider class of problems. Each of these papers uses a bound on the potential energy of the non-radiating motion relative to its kinetic energy; as these quantities are equal a contradiction is established. However, this approach cannot be employed directly in two dimensions when there are two surface-piercing bodies, essentially because the free surface between the bodies is separated (by the bodies) from both ±∞. The purpose of the present work is to show how a conformal mapping can be used to help to derive a bound on this part of the potential energy, and thereby prove uniqueness; the end result is that the solution will be unique provided the frequency is no greater than a parameter which depends on the geometry. © Oxford University Press Articles nationallicence KUZNETSOV N. G. Institute for Engineering Studies, Russian Academy of Sciences, POMI, Fontanka 27, 191011 St Petersburg, Russia, Manchester, Oxford Road, Manchester M139PL aut SIMON M. J. Department of Mathematics, University of Manchester Manchester, Oxford Road, Manchester M139PL aut The Quarterly Journal of Mechanics and Applied Mathematics Oxford University Press 48/4(1995-11), 507-515 0033-5614 48:4<507 1995 48 qjmamj https://doi.org/10.1093/qjmam/48.4.507 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1093/qjmam/48.4.507 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- KUZNETSOV N. G. Institute for Engineering Studies, Russian Academy of Sciences, POMI, Fontanka 27, 191011 St Petersburg, Russia, Manchester, Oxford Road, Manchester M139PL aut NATIONALLICENCE 700 1- SIMON M. J. Department of Mathematics, University of Manchester Manchester, Oxford Road, Manchester M139PL aut NATIONALLICENCE 773 0- The Quarterly Journal of Mechanics and Applied Mathematics Oxford University Press 48/4(1995-11), 507-515 0033-5614 48:4<507 1995 48 qjmamj Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford