Geodesic
On the Strong Solutions of a Regularized Model of a Nonlinear Visco-Elastic Medium
Matematičeskie zametki, Tome 84 (2008) no. 2, pp. 238-253

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We consider the initial boundary-value problem for the system of equations describing the motion of a nonlinear visco-elastic medium with memory along the trajectories of the velocity field; the system in question is a generalization of the system of Navier–Stokes equations. We establish existence and uniqueness theorems for strong solutions containing higher derivatives that are square-integrable in the plane case.
Keywords: nonlinear visco-elastic medium, Navier–Stokes equations, initial boundary-value problem, existence and uniqueness theorem, regularization, Sobolev space. 
@article{MZM_2008_84_2_a6,
     author = {V. P. Orlov},
     title = {On the {Strong} {Solutions} of a {Regularized} {Model} of a {Nonlinear} {Visco-Elastic} {Medium}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {238--253},
     publisher = {mathdoc},
     volume = {84},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_2_a6/}
}
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V. P. Orlov. On the Strong Solutions of a Regularized Model of a Nonlinear Visco-Elastic Medium. Matematičeskie zametki, Tome 84 (2008) no. 2, pp. 238-253. http://geodesic.mathdoc.fr/item/MZM_2008_84_2_a6/