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 CMFD, 2007, Volume 21, Pages 133–148 (Mi cmfd81)

On the estimate of lifetime for solutions of the Cauchy–Kovalevskaya system with examples in hydrodynamics of ideal fluid with free surface

R. V. Shamin

P. P. Shirshov institute of Oceanology of RAS

Abstract: Equations describing nonstationary flow of ideal fluid with free surface are considered. They are investigated in conformal variables. For such equations, the correct solvability is proved in a scale of spaces of analytic functions. Constructive methods of estimation of lifetime of solutions for such equations are developed and justified. An example of numerical calculation by these methods is given.

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English version:
Journal of Mathematical Sciences, 2008, 153:5, 612–628

Bibliographic databases:

UDC: 517.957

Citation: R. V. Shamin, “On the estimate of lifetime for solutions of the Cauchy–Kovalevskaya system with examples in hydrodynamics of ideal fluid with free surface”, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), CMFD, 21, PFUR, M., 2007, 133–148; Journal of Mathematical Sciences, 153:5 (2008), 612–628

Citation in format AMSBIB
\Bibitem{Sha07} \by R.~V.~Shamin \paper On the estimate of lifetime for solutions of the Cauchy--Kovalevskaya system with examples in hydrodynamics of ideal fluid with free surface \inbook Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A.~L.~Skubachevskii (Peoples' Friendship University of Russia) \serial CMFD \yr 2007 \vol 21 \pages 133--148 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd81} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2336495} \zmath{https://zbmath.org/?q=an:1159.35401} \transl \jour Journal of Mathematical Sciences \yr 2008 \vol 153 \issue 5 \pages 612--628 \crossref{https://doi.org/10.1007/s10958-008-9139-7} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-54249136226} 

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This publication is cited in the following articles:
1. Korobkov M.V., “Necessary and sufficient conditions for the unique determination of plane domains”, Doklady Mathematics, 76:2 (2007), 722–723
2. R. V. Shamin, “Dynamics of ideal liquid with free surface in conformal variables”, Journal of Mathematical Sciences, 160:5 (2009), 537–678
3. R. V. Shamin, “Approximation of Evolution Differential Equations in Scales of Hilbert Spaces”, Math. Notes, 85:2 (2009), 293–295
4. R. V. Shamin, “Surface waves on the water of minimal smoothness”, Journal of Mathematical Sciences, 170:3 (2010), 356–370
5. Shamin R.V., “Modelirovanie voln-ubiits na osnove evolyutsionnykh differentsialnykh vklyuchenii”, Fundamentalnaya i prikladnaya gidrofizika, 5:1 (2012), 14–23
6. Badulin S.I., Ivonin D.V., “Trekhmernye volny-ubiitsy. esche raz o novogodnei volne”, Fundamentalnaya i prikladnaya gidrofizika, 5:1 (2012), 37–51
7. Gorlenko A.V., Smirnova A.I., Shamin R.V., Yudin A.V., “Chislennoe modelirovanie voln-ubiits v okeane”, Vestnik rossiiskogo universiteta druzhby narodov. seriya: matematika, informatika, fizika, 2013, no. 1, 111–119
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