Global Existence for the Multi-Dimensional Compressible Viscoelastic flows
arXiv:1010.4351
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.