# American Institute of Mathematical Sciences

March  2015, 35(3): 917-934. doi: 10.3934/dcds.2015.35.917

## The initial-boundary value problem for the compressible viscoelastic flows

 1 Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States 2 Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260

Received  March 2014 Revised  March 2014 Published  October 2014

The initial-boundary value problem for the equations of compressible viscoelastic flows is considered in a bounded domain of three-dimensional spatial dimensions. The global existence of strong solution near equilibrium is established. Uniform estimates in $W^{1,q}$ with $q>3$ on the density and deformation gradient are also obtained.
Citation: Xianpeng Hu, Dehua Wang. The initial-boundary value problem for the compressible viscoelastic flows. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 917-934. doi: 10.3934/dcds.2015.35.917
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