Geodesic
On weak solvability of fractional models of viscoelastic high order fluid
Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 54-76

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In this paper, we establish the existence of a weak solution to the initial boundary value problem for the motion equations of viscoelastic incompressible fluid with constitutive law containing high-order fractional derivatives and with memory along the trajectories of the velocity field. The proof is by approximation of the original problem by a sequence of regularized problems followed by a passage to the limit based on appropriate a priori estimates. Methods of the theory of fractional derivatives calculus and the theory of regular Lagrangian flows (generalization of the classical solution of ODE systems) are used.
Keywords: viscoelastic medium, fractional derivative, initial boundary value problem, weak solution, regular Lagrangian flow.
Mots-clés : motion equations 
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     title = {On weak solvability of fractional models of viscoelastic high order fluid},
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V. G. Zvyagin; V. P. Orlov. On weak solvability of fractional models of viscoelastic high order fluid. Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 54-76. http://geodesic.mathdoc.fr/item/IM2_2024_88_1_a3/