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

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Matematicheskie Zametki, 2008, Volume 84, Issue 2, Pages 238–253
DOI: https://doi.org/10.4213/mzm4067 (Mi mzm4067)

This article is cited in 14 scientific papers (total in 14 papers)

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

V. P. Orlov

Voronezh State University

Full-text PDF (523 kB) Citations (14)

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

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.

Received: 14.03.2007

English version:
Mathematical Notes, 2008, Volume 84, Issue 2, Pages 224–238
DOI: https://doi.org/10.1134/S0001434608070237

Bibliographic databases:

UDC: 517.958

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/mzm4067

https://doi.org/10.4213/mzm4067

https://www.mathnet.ru/eng/mzm/v84/i2/p238

This publication is cited in the following 14 articles:

V. G. Zvyagin, V. P. Orlov, “On weak solvability of fractional models of viscoelastic high order fluid”, Izv. Math., 88:1 (2024), 54–76
V. G. Zvyagin, A. V. Zvyagin, V. P. Orlov, M. V. Turbin, “On the Weak Solvability of High-order Viscoelastic Fluid Dynamics Model”, Lobachevskii J Math, 45:4 (2024), 1524
E. I. Kostenko, “Investigation of Weak Solvability of One Model Nonlinear Viscosity Fluid”, Lobachevskii J Math, 45:4 (2024), 1421
Zvyagin V., Orlov V., “On Strong Solutions of Fractional Nonlinear Viscoelastic Model of Voigt Type”, Math. Meth. Appl. Sci., 44:15 (2021), 11768–11782
Zvyagin V.G., Orlov V.P., “Weak Solvability of One Viscoelastic Fractional Dynamics Model of Continuum With Memory”, J. Math. Fluid Mech., 23:1 (2021), 9
Plokhaya V E., “On Small Motions of Hydrodynamic Systems Containing a Viscoelastic Fluid”, Lobachevskii J. Math., 42:5, SI (2021), 996–1013
V. G. Zvyagin, V. P. Orlov, “On regularity of weak solutions to a generalized Voigt model of viscoelasticity”, Comput. Math. Math. Phys., 60:11 (2020), 1872–1888
V. G. Zvyagin, V. P. Orlov, “On strong solutions of a fractional nonlinear viscoelastic Voigt-type model”, Russian Math. (Iz. VUZ), 63:12 (2019), 96–100
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
Victor Zvyagin, Vladimir Orlov, AIP Conference Proceedings, 1759, 2016, 020040
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
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
Vladimir Orlov, “On Strong Solutions of Regularized Model of a Viscoelastic Medium with Variable Boundary”, ISRN Mathematical Physics, 2012 (2012), 1
V. P. Orlov, “Strong solution of certain thermoviscoelastic system”, Russian Math. (Iz. VUZ), 54:8 (2010), 41–47

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

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References:	79
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