Global Existence for the Multi-Dimensional Compressible Viscoelastic flows

2010/10/21 by Xianpeng Hu, Dehua Wang, Hu, Xianpeng +1 · 4 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.1010.4351

arxiv created 2010/10/21 · openalex publication_date 2010/10/21 · arxiv updated 2010/10/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces. Using uniform estimates for a hyperbolic-parabolic linear system with convection terms, we prove the global existence in the Besov space which is invariant with respect to the scaling of the associated equations. Several important estimates are achieved, including a smoothing effect on the velocity, and the L¹-decay of the density and deformation gradient.

Citations

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

Cited by

• Diffusion wave phenomena and optimal time decay for incompressible viscoelastic flows
• Global existence and stability of near-affine solutions of compressible elastodynamics
• Decay estimates for the compressible viscoelastic equations in an exterior domain
• Local energy decay of solutions to the linearized compressible viscoelastic system around motionless state in an exterior domain

Related

• Global existence in critical spaces for density-dependent incompressible viscoelastic fluids
• Global existence in critical spaces for incompressible viscoelastic fluids
• The initial-boundary value problem for the compressible viscoelastic fluids
• Large time behavior in critical L^p Besov spaces for compressible viscoelastic flows
• Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows