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

Сибирский математический журнал

V. G. Zvyagin¹ 

[1] Voronezh State University

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

DOI  :  10.1134/S0037446618060101

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

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.

【 授权许可】

CC BY