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

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.

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Correspondence to V. G. Zvyagin.

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Original Russian Text © 2018 Zvyagin V.G. and Orlov V.P.

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Voronezh. Translated from Sibirskii Matematicheskii Zhurnal, vol. 59, no. 6, pp. 1351–1369, November–December, 2018; DOI: 10.17377/smzh.2018.59.610.

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Zvyagin, V.G., Orlov, V.P. On Solvability of an Initial-Boundary Value Problem for a Viscoelasticity Model with Fractional Derivatives. Sib Math J 59, 1073–1089 (2018). https://doi.org/10.1134/S0037446618060101

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  • DOI: https://doi.org/10.1134/S0037446618060101

Keywords

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