Geodesic
The weak solvability of an inhomogeneous dynamic problem
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 1, pp. 93-99

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The existence of a weak solution to the initial boundary value problem for the equations of motion of a viscoelastic fluid with memory along the trajectories of a nonsmooth velocity field with inhomogeneous boundary condition is proved. The analysis involves Galerkin-type approximations of the original problem followed by the passage to the limit based on a priori estimates. To study the behavior of trajectories of a nonsmooth velocity field, the theory of regular Lagrangian flows is used.
Keywords: viscoelastic continuum, a priori estimate, weak solution, regular Lagrangian flow, trajectory. 
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     author = {V. G. Zvyagin and V. P. Orlov},
     title = {The weak solvability of an inhomogeneous dynamic problem},
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     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2023_57_1_a7/}
}
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V. G. Zvyagin; V. P. Orlov. The weak solvability of an inhomogeneous dynamic problem. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 1, pp. 93-99. http://geodesic.mathdoc.fr/item/FAA_2023_57_1_a7/