Geodesic
Concentration of frequencies of trapped waves in problems on freely floating bodies
Sbornik. Mathematics, Tome 203 (2012) no. 9, pp. 1269-1294 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that by choosing the shape of two identical bodies floating freely in a channel with symmetric cross-section it is possible to form any pre-assigned number of linearly independent trapped waves (localized solutions). Bibliography: 27 titles.
Keywords: trapped surface waves, trapped modes, localized solutions, freely floating body, concentration of the point spectrum. 
@article{SM_2012_203_9_a2,
     author = {S. A. Nazarov},
     title = {Concentration of frequencies of trapped waves in problems on freely floating bodies},
     journal = {Sbornik. Mathematics},
     pages = {1269--1294},
     year = {2012},
     volume = {203},
     number = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_9_a2/}
}
TY  - JOUR
AU  - S. A. Nazarov
TI  - Concentration of frequencies of trapped waves in problems on freely floating bodies
JO  - Sbornik. Mathematics
PY  - 2012
SP  - 1269
EP  - 1294
VL  - 203
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/SM_2012_203_9_a2/
LA  - en
ID  - SM_2012_203_9_a2
ER  - 
%0 Journal Article
%A S. A. Nazarov
%T Concentration of frequencies of trapped waves in problems on freely floating bodies
%J Sbornik. Mathematics
%D 2012
%P 1269-1294
%V 203
%N 9
%U http://geodesic.mathdoc.fr/item/SM_2012_203_9_a2/
%G en
%F SM_2012_203_9_a2
S. A. Nazarov. Concentration of frequencies of trapped waves in problems on freely floating bodies. Sbornik. Mathematics, Tome 203 (2012) no. 9, pp. 1269-1294. http://geodesic.mathdoc.fr/item/SM_2012_203_9_a2/

[1] F. John, “On the motion of floating bodies. I”, Comm. Pure Appl. Math., 2:1 (1949), 13–57 | DOI | MR | Zbl

[2] F. John, “On the motion of floating bodies. II. Simple harmonic motions”, Comm. Pure Appl. Math., 3:1 (1950), 45–101 | DOI | MR

[3] A.-S. Bonnet-Ben Dhia, P. Joly, “Mathematical analysis of guided water waves”, SIAM J. Appl. Math., 53:6 (1993), 1507–1550 | DOI | MR | Zbl

[4] C. M. Linton, P. McIver, “Embedded trapped modes in water waves and acoustics”, Wave Motion, 45:1–2 (2007), 16–29 | DOI | MR | Zbl

[5] N. Kuznetsov, V. Maz'ya, B. Vainberg, Linear water waves, Cambridge Univ. Press, Cambridge, 2002 | MR | Zbl

[6] D. A. Indeitsev, N. G. Kuznetsov, O. V. Motygin, Yu. A. Mochalova, Lokalizatsiya lineinykh voln, Izd-vo S.-Peterb. un-ta, SPb., 2007

[7] P. McIver, M. McIver, “Trapped modes in the water-wave problem for a freely floating structure”, J. Fluid Mech., 558 (2006), 53–67 | DOI | MR | Zbl

[8] R. Porter, D. V. Evans, “Examples of trapped modes in the presence of freely floating structures”, J. Fluid Mech., 606 (2008), 189–207 | DOI | MR | Zbl

[9] R. Porter, D. V. Evans, “Water-wave trapping by floating circular cylinders”, J. Fluid Mech., 633 (2009), 311–325 | DOI | MR | Zbl

[10] N. Kuznetsov, “On the problem of time-harmonic water waves in the presence of a freely-floating structure”, St. Petersburg Math. J., 22:6 (2011), 985–995 | DOI | MR | Zbl

[11] S. A. Nazarov, “Concentration of trapped modes in problems of the linearized theory of water waves”, Sb. Math., 199:12 (2008), 1783–1807 | DOI | MR | Zbl

[12] S. A. Nazarov, “Simple method for finding trapped modes in problems of the linear theory of surface waves”, Dokl. Math., 80:3 (2009), 914–917 | DOI | MR | Zbl

[13] S. A. Nazarov, “Sufficient conditions on the existence of trapped modes in problems of the linear theory of surface waves”, J. Math. Sci. (N. Y.), 167:5 (2010), 713–725 | DOI | MR

[14] S. A. Nazarov, J. H. Videman, “Trapping of water waves by freely floating structures in a channel”, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 467:2136 (2011), 3613–3632 | DOI | MR

[15] S. A. Nazarov, “Incomplete comparison principle in problems about surface waves trapped by fixed and freely floating bodies”, J. Math. Sci. (N. Y.), 175:3 (2011), 309–348 | DOI | MR

[16] D. V. Evans, M. Levitin, D. Vassiliev, “Existence theorems for trapped modes”, J. Fluid Mech., 261 (1994), 21–31 | DOI | MR | Zbl

[17] S. A. Nazarov, Asimptoticheskaya teoriya tonkikh plastin i sterzhnei. Ponizhenie razmernosti i integralnye otsenki, Nauchnaya kniga, Novosibirsk, 2002

[18] M. S. Birman, M. Z. Solomyak, Spectral-theory of self-adjoint operators in Hilbert space, Math. Appl. (Soviet Ser.), Kluwer Acad. Publ., Dordrecht, 1987 | MR | MR | Zbl

[19] Ch. C. Mei, M. Stiassnie, D. K.-P. Yue, Theory and applications of ocean surface waves. Part 1. Linear aspects, Adv. Ser. Ocean Eng., 23, World Scientific, Hackensack, NJ, 2005 | MR | Zbl

[20] L. Euler, Theorie complette (sic) de la construction et de la manoeuvre des vaisseaux, Imperial Academy of Sciences, St.-Petersburg, 1773

[21] S. A. Nazarov, “Concentration of the point spectrum on the continuous one in problems of linear water-wave theory”, J. Math. Sci. (N. Y.), 152:5 (2008), 674–689 | DOI | MR

[22] G. Cardone, T. Durante, S. A. Nazarov, “Water-waves modes trapped in a canal by a near-surface rough body”, ZAMM Z. Angew. Math. Mech., 90:12 (2010), 983–1004 | DOI | MR | Zbl

[23] S. A. Nazarov, “A body traps as many water-wave modes in a symmetric channel as it wishes”, Russ. J. Math. Phys., 18:2 (2011), 183–194 | DOI | MR

[24] O. A. Ladyzhenskaya, The boundary value problems of mathematical physics, Appl. Math. Sci., 49, Springer–Verlag, New York, 1985 | MR | MR | Zbl | Zbl

[25] I. Ts. Gokhberg, M. G. Krein, Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965 ; I. C. Gohberg, M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Transl. Math. Monogr., 18, Amer. Math. Soc., Providence, RI, 1969 | MR | MR | Zbl

[26] I. V. Kamotskii, S. A. Nazarov, “Exponentially decreasing solutions of diffraction problems on a rigid periodic boundary”, Math. Notes, 73:1–2 (2003), 129–131 | DOI | MR | Zbl

[27] S. A. Nazarov, “Asymptotic solution of the Navier–Stokes problem on the flow of a thin layer of fluid”, Siberian Math. J., 31:2 (1990), 296–307 | DOI | MR | Zbl