On weak solvability of fractional models of viscoelastic high order fluid

V. G. Zvyagin ; V. P. Orlov

Izvestiya. Mathematics , Tome 88 (2024) no. 1, pp. 54-76.

Résumé

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.

Détail

Keywords: viscoelastic medium, fractional derivative, initial boundary value problem, weak solution, regular Lagrangian flow.
Mots-clés : motion equations

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