Global Existence for the Multi-Dimensional Compressible Viscoelastic flows

By Xianpeng Hu, Dehua Wang. 2010

143 citations recorded by the source corpus.

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 $L^1-$decay of the density and deformation gradient.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d1d91747c93b8ff3df6dab1a904199173419f42b