Global wellposedness to the $n$-dimensional compressible Oldroyd-B model without damping mechanism

Abstract

The Cauchy problem of the compressible Oldroyd-B model without damping mechanism in R^n$with$n\ge2$ is considered. The lack of dissipation in density and stress tensor in the model is compensated by exploiting an intrinsic structure and introducing new quantities between density, velocity and stress tensor. Therefore, global solutions to the system with small initial data in critical Besov spaces are obtained. As a byproduct, optimal time decay rates of the solutions are derived by using an energy estimation argument. The results remain valid for the compressible viscoelastic system without the `div-curl structure assumption and thus improve those given by Hu and Wang [ J. Differential Equations, {\bf 250}, 1200--1231, 2011] and Qian and Zhang [Arch. Ration. Mech. Anal., {\bf 198}, 835--868, 2010].

36pages

References in corpus (4)

• Global solutions to the $n$-dimensional incompressible Oldroyd-B model without damping mechanism
• Global existence in critical spaces for non Newtonian compressible viscoelastic flows
• Global classical solutions of 3D compressible viscoelastic system near equilibrium
• Optimal decay for the compressible Navier-Stokes equations without additional smallness assumptions

Cited by in corpus (1)

• Global wellposedness and large time behavior of solutions to the $n$-dimensional compressible Oldroyd-B model