# American Institute of Mathematical Sciences

November  2018, 23(9): 3855-3877. doi: 10.3934/dcdsb.2018114

## On one problem of viscoelastic fluid dynamics with memory on an infinite time interval

 Research Institute of Mathematics, Voronezh State University, Universitetskaya pl., 1, Voronezh 394 018, Russia

* Corresponding author: Victor Zvyagin

Received  March 2017 Revised  June 2017 Published  April 2018

Fund Project: The research of the first author was supported by the Russian Science Foundation (project no. 16-11-10125, Lemma 3.4). The research of the second author was supported by the Ministry of Education and Science of the Russian Federation (grant 14.Z50.31.0037).

In the present paper we establish the existence of weak solutions of one boundary value problem for one model of a viscoelastic fluid with memory along the trajectories of the velocity field on an infinite time interval. We use solvability of related approximating initial-boundary value problems on finite time intervals and responding pass to the limit.

Citation: Victor Zvyagin, Vladimir Orlov. On one problem of viscoelastic fluid dynamics with memory on an infinite time interval. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3855-3877. doi: 10.3934/dcdsb.2018114
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