Global Existence for the Multi-Dimensional Compressible Viscoelastic flows
Analysis of PDEs
2010-10-22 v1
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 decay of the density and deformation gradient.
Cite
@article{arxiv.1010.4351,
title = {Global Existence for the Multi-Dimensional Compressible Viscoelastic flows},
author = {Xianpeng Hu and Dehua Wang},
journal= {arXiv preprint arXiv:1010.4351},
year = {2010}
}