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Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 115, Pages 191–202
(Mi znsl4051)
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This article is cited in 40 scientific papers (total in 40 papers)
Theory of nonstationary flows of Kelvin–Voigt fluids
A. P. Oskolkov
Abstract:
One proves the global unique solvability in class $W_\infty^1(0,T;C^{2,\alpha}(\overline\Omega)\cap H(\Omega))$ of the initial-boundary-value problem for the quasilinear system
$$
\frac{\partial\vec v}{\partial t}+v_k\frac{\partial\vec v}{\partial x_k}-\mu_1\frac{\partial\Delta\vec v}{\partial t}-\mu_0\Delta\vec v-\int_0^tK(t-\tau)\Delta\vec v(\tau)d\tau+\operatorname{grad}p=\vec f,\qquad\operatorname{div}\vec v=0,\quad\mu_1>0.
$$
This system described the nonstationary flows of the elastic-viscous Kelvin-Voigt fluids with defining relation
$$
\Bigl(1+\sum_{l=1}^L\lambda_l\frac{\partial^l}{\partial t^l}\Bigr)\sigma=2\Bigl(\nu+\sum_{m=1}^{L+1}\varkappa_m\frac{\partial^m}{\partial t^m}\Bigr)D,\qquad L=0,1,2,\dots;\quad\lambda_L,\varkappa_{L+1}>0.
$$
Citation:
A. P. Oskolkov, “Theory of nonstationary flows of Kelvin–Voigt fluids”, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Zap. Nauchn. Sem. LOMI, 115, "Nauka", Leningrad. Otdel., Leningrad, 1982, 191–202; J. Soviet Math., 28:5 (1985), 751–758
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https://www.mathnet.ru/eng/znsl4051 https://www.mathnet.ru/eng/znsl/v115/p191
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