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Mat. Zametki, 2008, Volume 84, Issue 2, Pages 238–253 (Mi mz4067)  

This article is cited in 5 scientific papers (total in 5 papers)

On the Strong Solutions of a Regularized Model of a Nonlinear Visco-Elastic Medium

V. P. Orlov

Voronezh State University

Abstract: We consider the initial boundary-value problem for the system of equations describing the motion of a nonlinear visco-elastic medium with memory along the trajectories of the velocity field; the system in question is a generalization of the system of Navier–Stokes equations. We establish existence and uniqueness theorems for strong solutions containing higher derivatives that are square-integrable in the plane case.

Keywords: nonlinear visco-elastic medium, Navier–Stokes equations, initial boundary-value problem, existence and uniqueness theorem, regularization, Sobolev space

DOI: https://doi.org/10.4213/mzm4067

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English version:
Mathematical Notes, 2008, 84:2, 224–238

Bibliographic databases:

UDC: 517.958
Received: 14.03.2007

Citation: V. P. Orlov, “On the Strong Solutions of a Regularized Model of a Nonlinear Visco-Elastic Medium”, Mat. Zametki, 84:2 (2008), 238–253; Math. Notes, 84:2 (2008), 224–238

Citation in format AMSBIB
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\by V.~P.~Orlov
\paper On the Strong Solutions of a Regularized Model of a Nonlinear Visco-Elastic Medium
\jour Mat. Zametki
\yr 2008
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\pages 238--253
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\pages 224--238
\crossref{https://doi.org/10.1134/S0001434608070237}
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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. V. P. Orlov, “Strong solution of certain thermoviscoelastic system”, Russian Math. (Iz. VUZ), 54:8 (2010), 41–47  mathnet  crossref  mathscinet
    2. V. P. Orlov, M. I. Parshin, “On one problem of dynamics of thermoviscoelastic medium of Oldroid type”, Russian Math. (Iz. VUZ), 58:5 (2014), 57–62  mathnet  crossref
    3. V. P. Orlov, M. I. Parshin, “On a problem in the dynamics of a thermoviscoelastic medium with memory”, Comput. Math. Math. Phys., 55:4 (2015), 650–665  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Zvyagin V.G. Orlov V.P., “Solvability of One Non-Newtonian Fluid Dynamics Model With Memory”, Nonlinear Anal.-Theory Methods Appl., 172 (2018), 73–98  crossref  mathscinet  zmath  isi  scopus
    5. V. G. Zvyagin, V. P. Orlov, “O silnykh resheniyakh drobnoi nelineino-vyazkouprugoi modeli tipa Foigta”, Izv. vuzov. Matem., 2019, no. 12, 106–111  mathnet  crossref
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