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Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 4, Pages 774–809 (Mi izv1075)  

This article is cited in 2 scientific papers (total in 2 papers)

On a system of equations describing surface waves

P. I. Naumkin, I. A. Shishmarev


Abstract: A new system of equations is proposed which describes surface waves in a fluid. The basic conservation laws are found for this system. The Cauchy problem for this system is considered, and the existence of a global solution (in time), the breakdown of a solution in finite time, and the smoothing of a discontinuous initial perturbation are studied.

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English version:
Mathematics of the USSR-Izvestiya, 1991, 37:1, 119–156

Bibliographic databases:

UDC: 517.958
MSC: 35Q20, 76B15
Received: 14.12.1987

Citation: P. I. Naumkin, I. A. Shishmarev, “On a system of equations describing surface waves”, Izv. Akad. Nauk SSSR Ser. Mat., 54:4 (1990), 774–809; Math. USSR-Izv., 37:1 (1991), 119–156

Citation in format AMSBIB
\Bibitem{NauShi90}
\by P.~I.~Naumkin, I.~A.~Shishmarev
\paper On a system of equations describing surface waves
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1990
\vol 54
\issue 4
\pages 774--809
\mathnet{http://mi.mathnet.ru/izv1075}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1073086}
\zmath{https://zbmath.org/?q=an:0759.35038|0721.35056}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..37..119N}
\transl
\jour Math. USSR-Izv.
\yr 1991
\vol 37
\issue 1
\pages 119--156
\crossref{https://doi.org/10.1070/IM1991v037n01ABEH002055}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. I. Naumkin, I. A. Shishmarev, “Asymptotic for large time of solutions of a system of equations for surface waves”, Math. USSR-Izv., 38:3 (1992), 525–551  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. P. I. Naumkin, I. A. Shishmarev, “Asymptotic Representation of Surface Waves in the Form of Two Traveling Burgers Waves”, Funct. Anal. Appl., 29:3 (1995), 168–179  mathnet  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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