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

This article is cited in 7 scientific papers (total in 7 papers)

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  crossref  mathscinet  zmath  isi  elib
    2. R. V. Shamin, “Dynamics of ideal liquid with free surface in conformal variables”, Journal of Mathematical Sciences, 160:5 (2009), 537–678  mathnet  crossref  mathscinet  zmath  elib
    3. R. V. Shamin, “Approximation of Evolution Differential Equations in Scales of Hilbert Spaces”, Math. Notes, 85:2 (2009), 293–295  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. R. V. Shamin, “Surface waves on the water of minimal smoothness”, Journal of Mathematical Sciences, 170:3 (2010), 356–370  mathnet  crossref  mathscinet
    5. Shamin R.V., “Modelirovanie voln-ubiits na osnove evolyutsionnykh differentsialnykh vklyuchenii”, Fundamentalnaya i prikladnaya gidrofizika, 5:1 (2012), 14–23  elib
    6. Badulin S.I., Ivonin D.V., “Trekhmernye volny-ubiitsy. esche raz o novogodnei volne”, Fundamentalnaya i prikladnaya gidrofizika, 5:1 (2012), 37–51  mathscinet  elib
    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  elib
  • Современная математика. Фундаментальные направления
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