Abstract:
In the paper, the settings of initial-boundary and initial value problems arising in a number of models of movement of nonlinearly viscous or viscoelastic incompressible fluid are considered, and existence theorems for these problems are presented. In particular, the settings of initial-boundary value problems appearing in the regularized model of the movement of viscoelastic fluid with Jeffris constitutive relation are described. The theorems for the existence of weak and strong solutions for these problems in bounded domains are given. The initial value problem for a nonlinearly viscous fluid on the whole space is considered. The estimates on the right-hand side and initial conditions under which there exist local and global solutions of this problem are presented. The modification of Litvinov's model for laminar and turbulent flows with a memory is described. The existence theorem for weak solutions of initial-boundary value problem appearing in this model is given.
Citation:
V. G. Zvyagin, “On Solvability of Some Initial-Boundary Problems for Mathematical Models of the Motion of Nonlinearly Viscous and Viscoelastic Fluids”, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 2, CMFD, 2, MAI, M., 2003, 57–69; Journal of Mathematical Sciences, 124:5 (2004), 5321–5334
\Bibitem{Zvy03}
\by V.~G.~Zvyagin
\paper On Solvability of Some Initial-Boundary Problems for Mathematical Models of the Motion of Nonlinearly Viscous and Viscoelastic Fluids
\inbook Proceedings of the International Conference on Differential and Functional-Differential Equations --- Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11--17 August, 2002). Part~2
\serial CMFD
\yr 2003
\vol 2
\pages 57--69
\publ MAI
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd21}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2129135}
\zmath{https://zbmath.org/?q=an:1128.76319}
\transl
\jour Journal of Mathematical Sciences
\yr 2004
\vol 124
\issue 5
\pages 5321--5334
\crossref{https://doi.org/10.1023/B:JOTH.0000047357.93280.18}
Linking options:
https://www.mathnet.ru/eng/cmfd21
https://www.mathnet.ru/eng/cmfd/v2/p57
This publication is cited in the following 8 articles:
V. G. Zvyagin, V. P. Orlov, “Weak Solvability of One Viscoelastic Fractional Dynamics Model of Continuum with Memory”, J. Math. Fluid Mech., 23:1 (2021)
Vladimir P. Orlov, INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020), 2325, INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020), 2021, 020008
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 solvability of an initial-boundary value problem for a viscoelasticity model with fractional derivatives”, Siberian Math. J., 59:6 (2018), 1073–1089
V. G. Zvyagin, V. P. Orlov, “On the weak solvability of a fractional viscoelasticity model”, Dokl. Math., 98:3 (2018), 568–570
V.G. Zvyagin, V.P. Orlov, “Solvability of one non-Newtonian fluid dynamics model with memory”, Nonlinear Analysis, 172 (2018), 73
V. P. Orlov, D. A. Rode, M. A. Pliev, “Weak solvability of the generalized Voigt viscoelasticity model”, Siberian Math. J., 58:5 (2017), 859–874
V. G. Zvyagin, V. P. Orlov, “On a model of thermoviscoelasticity of Jeffreys–Oldroyd type”, Comput. Math. Math. Phys., 56:10 (2016), 1803–1812
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