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Global Existence for the Multi-Dimensional Compressible Viscoelastic flows
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
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