Geodesic
Nonlocal problems for the equations of Kelvin--Voight fluids and their $\varepsilon$-approximations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Tome 221 (1995), pp. 185-207

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In this paper, we study some nonlocal problems for the Kelvin–Voight equations (1) and the penalized Kelvin–Voight equations (2): the first and second initial boundary-value problems and the first and second time periodic boundary problems. We prove that these problems have global smooth solutions of the class $W^1_\infty(\mathbb R^+;W_2^{2+k}(\Omega))$, $k=1,2,\dots$; $\Omega\subset\mathbb R^3$. Bibliography: 25 titles. 
@article{ZNSL_1995_221_a11,
     author = {A. P. Oskolkov},
     title = {Nonlocal problems for the equations of {Kelvin--Voight} fluids and their $\varepsilon$-approximations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {185--207},
     publisher = {mathdoc},
     volume = {221},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a11/}
}
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A. P. Oskolkov. Nonlocal problems for the equations of Kelvin--Voight fluids and their $\varepsilon$-approximations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Tome 221 (1995), pp. 185-207. http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a11/