Geodesic
Apriori estimates on the semiaxis $t\geqslant0$ for solutions of equations of motion of linear viscoelastic fluids with infinite Dirichlet integral and their applications
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 21, Tome 182 (1990), pp. 86-101

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Global solvability on the semiaxis $t\geqslant0$ initial value problems for equations of motion of linear viscoelastic fluids with following external forse $f(x,t):f,f_t\in L_\infty(\mathrm{R}^+;L_2(\Omega))$ is investigated. Existence time periodicity of “small” smooth stable solutions of equations of motion of Oldroyd type fluids and Kelvin–Voight type fluids with “small” time periodicity external forse $f$ is proved. 
@article{ZNSL_1990_182_a3,
     author = {A. A. Kotsiolis and A. P. Oskolkov and R. D. Shadiev},
     title = {Apriori estimates on the semiaxis $t\geqslant0$ for solutions of equations of motion of linear viscoelastic fluids with infinite {Dirichlet} integral and their applications},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {86--101},
     publisher = {mathdoc},
     volume = {182},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_182_a3/}
}
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A. A. Kotsiolis; A. P. Oskolkov; R. D. Shadiev. Apriori estimates on the semiaxis $t\geqslant0$ for solutions of equations of motion of linear viscoelastic fluids with infinite Dirichlet integral and their applications. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 21, Tome 182 (1990), pp. 86-101. http://geodesic.mathdoc.fr/item/ZNSL_1990_182_a3/