On a~solvability in general on $(0,\infty)$ a~main initial boundary-value problem for two-dimentional equations of Oldroyd fluid
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 16, Tome 156 (1986), pp. 69-72
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For the system
$$\begin{cases}
\frac{\partial\bar v}{\partial t}+v_k\frac{\partial\bar v}{\partial x_k}-\mu\Delta\bar v-\mathbb K\Delta\bar v+\operatorname{grad} p=\bar f(x,t),\\
\operatorname{div}\bar v=0,\;\mathbb K\bar v=\int_0^tK(t-\tau)v(\tau)\,d\tau,\;K=\sum c_je^{-\zeta_jt},\;c_j,\zeta_j>0
\end{cases}$$
described two-dimentional motion of Oldroyd liquiditis proved a global solvability for $t\in(0,\infty)$.
@article{ZNSL_1986_156_a6,
author = {N. A. Karazeeva},
title = {On a~solvability in general on $(0,\infty)$ a~main initial boundary-value problem for two-dimentional equations of {Oldroyd} fluid},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {69--72},
publisher = {mathdoc},
volume = {156},
year = {1986},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_156_a6/}
}
TY - JOUR AU - N. A. Karazeeva TI - On a~solvability in general on $(0,\infty)$ a~main initial boundary-value problem for two-dimentional equations of Oldroyd fluid JO - Zapiski Nauchnykh Seminarov POMI PY - 1986 SP - 69 EP - 72 VL - 156 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1986_156_a6/ LA - ru ID - ZNSL_1986_156_a6 ER -
%0 Journal Article %A N. A. Karazeeva %T On a~solvability in general on $(0,\infty)$ a~main initial boundary-value problem for two-dimentional equations of Oldroyd fluid %J Zapiski Nauchnykh Seminarov POMI %D 1986 %P 69-72 %V 156 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1986_156_a6/ %G ru %F ZNSL_1986_156_a6
N. A. Karazeeva. On a~solvability in general on $(0,\infty)$ a~main initial boundary-value problem for two-dimentional equations of Oldroyd fluid. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 16, Tome 156 (1986), pp. 69-72. http://geodesic.mathdoc.fr/item/ZNSL_1986_156_a6/