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September 2007 Global existence for a 2D incompressible viscoelastic model with small strain
Zhen Lei, Chun Liu, Yi Zhou
Commun. Math. Sci. 5(3): 595-616 (September 2007).


In this paper, we continue our previous study towards understanding the twodimensional hydrodynamic systems describing Oldroyd type incompressible viscoelastic fluids. We will decompose the deformation tensor into the strain and rotation components and look at their distinct contributions and structures in the small strain (with respect to viscosity) dynamics. In particular, we prove that there exist classical solutions globally in time if the strain component of the initial deformation is small enough, while we require no assumptions on smallness of the magnitude of the rotation component.


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Zhen Lei. Chun Liu. Yi Zhou. "Global existence for a 2D incompressible viscoelastic model with small strain." Commun. Math. Sci. 5 (3) 595 - 616, September 2007.


Published: September 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1132.76008
MathSciNet: MR2352333

Primary: 35M10 , 76D03 , 76D09

Keywords: incompressibility , partial dissipation system , small strain , viscoelasticity

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 3 • September 2007
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