On 2D Viscoelasticity with Small Strain

Abstract

An exact two-dimensional rotation-strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under the smallness assumptions only on the size of initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, which is revealed by passing the partial dissipation to the whole system.

Different contributions of strain and rotation of the deformation are studied for viscoelastic fluids of Oldroyd-B type in 2D

References in corpus (3)

• Global Solutions for Incompressible Viscoelastic Fluids
• Global Existence with Small Initial Data for Three-Dimensional Incompressible Isotropic Viscoelastic Materials
• Global Strong Solution to the Density-Dependent Incompressible Viscoelastic Fluids

Cited by in corpus (16)

• Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows
• Vanishing Viscosity Limit for Incompressible Viscoelasticity in Two Dimensions
• Optimal time-decay estimates for an Oldroyd-B model with zero viscosity
• Global regularity for the 2D Oldroyd-B model in the corotational case
• Global existence in critical spaces for non Newtonian compressible viscoelastic flows
• Global Well-posedness of Incompressible Elastodynamics in Two Dimensions
• A blow-up criterion for 3-D compressible visco-elasticity
• Global solution to the incompressible Oldroyd-B model in hybrid Besov spaces
• The initial-boundary value problem for the compressible viscoelastic fluids
• Global solution in critical spaces to the compressible Oldroyd-B model with non-small coupling parameter
• Global small solutions of 3D incompressible Oldroyd-B model without damping mechanism
• Well-posedness of a Parabolic-hyperbolic Keller-Segel System in the Sobolev Space Framework
• Global existence results for Oldroyd-B Fluids in exterior domains: The case of non-small coupling parameters
• Global Well-posedness of Incompressible Elastodynamics in Three Dimensional Thin Domain
• Global weak solutions for some Oldroyd models
• Global solutions to the Oldroyd-B model with a class of large initial data