Global Existence with Small Initial Data for Three-Dimensional Incompressible Isotropic Viscoelastic Materials

Abstract

Global existence for a system of nonlinear partial differential equations (PDE) modeling an isotropic incompressible viscoelastic material is proved. The structure of the PDE is derived through constitutive assumptions on the material. Restriction on the size of the initial displacement and velocity for the model is specified independent of the size of the viscosity of the material. The proof of global existence combines use of vector fields, local energy decay estimates, generalized Sobolev inequalities, and hyperbolic energy estimates.

44 pages

References in corpus (1)

• Global Solutions for Incompressible Viscoelastic Fluids

Cited by in corpus (9)

• On 2D Viscoelasticity with Small Strain
• Vanishing Viscosity Limit for Incompressible Viscoelasticity in Two Dimensions
• Uniform Bound of the Highest Energy for the 3D Incompressible Elastodynamics
• Global Well-posedness for the Three Dimensional Simplified Inertial Ericksen-Leslie Systems Near Equilibrium
• Global Existence for the Multi-Dimensional Compressible Viscoelastic flows
• Strong Solutions to the Three-Dimensional Compressible Viscoelastic Fluids
• Formation of singularity for compressible viscoelasticity
• Local Strong Solution to the Compressible Viscoelastic Fluid with Large Data
• Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows