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

被引：8

作者：

Zvyagin, V. G. ^{[1
]}

Orlov, V. P. ^{[1
]}

机构：

[1] Voronezh State Univ, Res Inst Math, Voronezh, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2018年 / 59卷 / 06期

关键词：

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

D O I：

10.1134/S0037446618060101

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：1073 / 1089

页数：17

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