On the Cauchy problems for certain regularized models to the incompressible viscoelastic flow

In this paper, we study the Cauchy problems for certain regularized models to the incompressible viscoelastic flow in n space dimensions with n=2,3. Firstly, we establish a regularity condition for the solution under ∇u∈L1(0,T;L∞(Rn)). Furthermore, we obtain a regularity condition to the smooth solu...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-04, Vol.43 (6), p.2999-3017
Main Authors: Qiu, Hua, Yao, Zheng‐an
Format: Article
Language:English
Subjects:
Cauchy problems
Computational fluid dynamics
Fluid flow
global regularity
Incompressible flow
Oldroyd model
Regularity
regularity criterion
regularization
Viscoelasticity
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Summary:In this paper, we study the Cauchy problems for certain regularized models to the incompressible viscoelastic flow in n space dimensions with n=2,3. Firstly, we establish a regularity condition for the solution under ∇u∈L1(0,T;L∞(Rn)). Furthermore, we obtain a regularity condition to the smooth solution for the inviscid regularized models in two space dimensions. Finally, we prove a global existence result of classical solutions for a three‐dimensional incompressible Oldroyd‐α model with fractional diffusion.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6097