Geodesic
On weak solutions to evolution equations of viscoelastic fluid flows
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 2, pp. 21-32

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We study the system of nonlinear equations describing unsteady flows of a viscoelastic fluid of Oldroyd type in a bounded three-dimensional domain with mixed boundary conditions. On one part of the boundary, the Navier slip condition is given, while on the other one, the no-slip condition is used. We prove the theorem on the existence, uniqueness, and energy estimates for weak solutions.
Keywords: initial boundary-value problem, weak solution, viscoelastic fluid, Oldroyd model, Navier slip boundary condition. 
@article{SJIM_2017_20_2_a2,
     author = {E. S. Baranovskii},
     title = {On weak solutions to evolution equations of viscoelastic fluid flows},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {21--32},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_2_a2/}
}
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E. S. Baranovskii. On weak solutions to evolution equations of viscoelastic fluid flows. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 2, pp. 21-32. http://geodesic.mathdoc.fr/item/SJIM_2017_20_2_a2/