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Mat. Zametki, 1998, Volume 63, Issue 3, Pages 442–450 (Mi mz1301)  

This article is cited in 8 scientific papers (total in 8 papers)

On the solvability of a nonstationary problem describing the dynamics of an incompressible viscoelastic fluid

G. A. Sviridyuka, T. G. Sukachevab

a Chelyabinsk State University
b Novgorod State Pedagogical Istitute

Abstract: We study the local solvability of the Cauchy–Dirichlet problem for the system
\begin{gather*} (1-\varkappa\nabla ^2)\mathbf v_t=\nu\nabla^2\mathbf v-(\mathbf v\cdot\nabla)\mathbf v-\nabla p+\mathbf f(t),
0=-\nabla(\nabla\cdot\mathbf v), \end{gather*}
which describes the dynamics of an incompressible viscoelastic Kelvin–Voigt fluid. The configuration space of the problem is described.

DOI: https://doi.org/10.4213/mzm1301

Full text: PDF file (215 kB)
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English version:
Mathematical Notes, 1998, 63:3, 388–395

Bibliographic databases:

UDC: 517.952
Received: 09.02.1993

Citation: G. A. Sviridyuk, T. G. Sukacheva, “On the solvability of a nonstationary problem describing the dynamics of an incompressible viscoelastic fluid”, Mat. Zametki, 63:3 (1998), 442–450; Math. Notes, 63:3 (1998), 388–395

Citation in format AMSBIB
\Bibitem{SviSuk98}
\by G.~A.~Sviridyuk, T.~G.~Sukacheva
\paper On the solvability of a nonstationary problem describing the dynamics of an incompressible viscoelastic fluid
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 3
\pages 442--450
\mathnet{http://mi.mathnet.ru/mz1301}
\crossref{https://doi.org/10.4213/mzm1301}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1631897}
\zmath{https://zbmath.org/?q=an:0915.76009}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 3
\pages 388--395
\crossref{https://doi.org/10.1007/BF02317787}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000075783100016}


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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. I. V. Burlachko, G. A. Sviridyuk, “An algorithm for solving the Cauchy problem for degenerate linear systems of ordinary differential equations”, Comput. Math. Math. Phys., 43:11 (2003), 1613–1619  mathnet  mathscinet  zmath
    2. V. E. Fedorov, P. N. Davydov, “Polulineinye vyrozhdennye evolyutsionnye uravneniya i nelineinye sistemy gidrodinamicheskogo tipa”, Tr. IMM UrO RAN, 19, no. 4, 2013, 267–278  mathnet  mathscinet  elib
    3. T. G. Sukacheva, A. O. Kondyukov, “On a class of Sobolev-type equations”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:4 (2014), 5–21  mathnet  crossref
    4. E. S. Baranovskii, “Flows of a polymer fluid in domain with impermeable boundaries”, Comput. Math. Math. Phys., 54:10 (2014), 1589–1596  mathnet  crossref  crossref  mathscinet  isi  elib
    5. N. A. Manakova, “Zadacha optimalnogo upravleniya dlya odnoi modeli dinamiki slaboszhimaemoi vyazkouprugoi zhidkosti”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:3 (2015), 22–29  mathnet  elib
    6. M. V. Plekhanova, “Quasilinear equations that are not solved for the higher-order time derivative”, Siberian Math. J., 56:4 (2015), 725–735  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. Sukacheva T.G., Matveeva O.P., “Taylor Problem For the Zero-Order Model of An Incompressible Viscoelastic Fluid”, Differ. Equ., 51:6 (2015), 783–791  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Plekhanova M.V., “Strong solutions of quasilinear equations in Banach spaces not solvable with respect to the highest-order derivative”, Discret. Contin. Dyn. Syst.-Ser. S, 9:3 (2016), 833–846  crossref  mathscinet  zmath  isi  elib  scopus
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