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On the Cauchy problems for certain regularized models to the incompressible viscoelastic flow
Author(s) -
Qiu Hua,
Yao Zhengan
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6097
Subject(s) - mathematics , inviscid flow , compressibility , viscoelasticity , mathematical analysis , space (punctuation) , cauchy distribution , initial value problem , flow (mathematics) , incompressible flow , cauchy problem , classical mechanics , geometry , physics , mechanics , linguistics , philosophy , thermodynamics
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 ∈ L 1 ( 0 , T ; L ∞ ( R n ) ) . 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.