Geodesic
Mixed initial-boundary value problem for equations of motion of Kelvin–Voigt fluids
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1371-1379

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The initial-boundary value problem for equations of motion of Kelvin–Voigt fluids with mixed boundary conditions is studied. The no-slip condition is used on some portion of the boundary, while the impermeability condition and the tangential component of the surface force field are specified on the rest of the boundary. The global-in-time existence of a weak solution is proved. It is shown that the solution is unique and depends continuously on the field of external forces, the field of surface forces, and initial data. 
@article{ZVMMF_2016_56_7_a14,
     author = {E. S. Baranovskii},
     title = {Mixed initial-boundary value problem for equations of motion of {Kelvin{\textendash}Voigt} fluids},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1371--1379},
     publisher = {mathdoc},
     volume = {56},
     number = {7},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a14/}
}
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E. S. Baranovskii. Mixed initial-boundary value problem for equations of motion of Kelvin–Voigt fluids. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1371-1379. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a14/