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Siberian Mathematical Journal

, Volume 59, Issue 6, pp 1073–1089 | Cite as

On Solvability of an Initial-Boundary Value Problem for a Viscoelasticity Model with Fractional Derivatives

  • V. G. ZvyaginEmail author
  • V. P. Orlov
Article
  • 7 Downloads

Abstract

We establish the existence and uniqueness (the latter only in the plane case) of a weak solution to an initial-boundary value problem for the system of the equations of motion of a viscoelastic fluid, namely, for the anti-Zener model whose constitutive law contains fractional derivatives. We use the approximation of this problem by a sequence of regularized Navier–Stokes systems and passage to the limit.

Keywords

viscoelastic medium equation of motion initial-boundary value problem weak solution anti-Zener model fractional derivative 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Research Institute of MathematicsVoronezh State UniversityVoronezhRussia

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