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Zapiski Nauchnykh Seminarov LOMI, 1979, Volume 84, Pages 185–210
(Mi znsl2942)
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This article is cited in 2 scientific papers (total in 2 papers)
Some model nonstationary systems in the theory of non-Newtonian fluids. II
A. P. Oskolkov
Abstract:
For the non-stationary quasi-linear system
\begin{gather*}
\frac{\partial\bar{v}}{\partial{t}}+v_k\frac{\partial{v}}{\partial{x_k}}+\lambda\biggl[\frac{\partial^2{\bar{v}}}{\partial t^2}+v_{kt}\bar{v}_{x_k}+v_k\frac{\partial^2\bar{v}}{\partial t\partial x_k}\biggr]-\nu\Delta\bar{v}-\varkappa\frac{\partial\Delta\bar v}{\partial t}+\biggl(1+\lambda\frac{\partial}{\partial t}\biggr)\operatorname{grad}p=\bar{F},
\\
\operatorname{div}\bar{v}=0
\end{gather*}
the local theorems of existence and uniqueness of generalized solutions with a finite energy integral
$$
\max_{0\leq t\leq T}\int_\Omega(\bar{v}^2_x+\bar{v}^2_t)\,dx
+\iint_{Q_T}\bar{v}^2_{xt}\,dx\,dt<+\infty;
$$
are proved. Different variants of regularized systems are constructed, for which the generalized solution
exists “in the large”.
Citation:
A. P. Oskolkov, “Some model nonstationary systems in the theory of non-Newtonian fluids. II”, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Zap. Nauchn. Sem. LOMI, 84, "Nauka", Leningrad. Otdel., Leningrad, 1979, 185–210; J. Soviet Math., 21:3 (1983), 383–399
Linking options:
https://www.mathnet.ru/eng/znsl2942 https://www.mathnet.ru/eng/znsl/v84/p185
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