Equations for Viscoelastic Fluids

Hu, Xianpeng; Lin, Fanghua; Liu, Chun

doi:10.1007/978-3-319-10151-4_25-1

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“…Further discussions of these topics can be referred to previous studies . A summary on some of the recent results can be found in a review paper …”

Section: Introductionmentioning

confidence: 99%

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

Qiu

Yao

2019

Math Methods in App Sciences

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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∈L1false(0,T;L∞false(double-struckRnfalse)false). 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.

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“…Further discussions of these topics can be referred to previous studies . A summary on some of the recent results can be found in a review paper …”

Section: Introductionmentioning

confidence: 99%