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

2009/03/16 by Paul Kessenich, Kessenich, Paul
Engineering · Mathematics · #35M10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.0903.2824

openalex publication_date 2009/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On almost global existence for nonrelativistic wave equations in 3D

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