Optimal time decay rate for compressible viscoelastic equations in critical spaces

Abstract

In this paper, we are concerned with the optimal time convergence rate of the global strong solution to some constant equilibrium states for the compressible viscoelastic fluids in the whole space. Green’s matrix method and energy estimate method are used to obtain the optimal time decay rate under the critical Besov space framework. Our result implies the optimal -time decay rate and only need the initial datum to be small in some critical Besov space which have very low regularity compared with the classical Sobolev space.

Keywords:

• Compressible viscoelastic fluids
• critical space framework
• optimal time decay

AMS Subject Classifications:

• 76N10
• 35Q35
• 35D35

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

J. Jia was supported by the National Natural Science Foundation of China [grant number 11501439]; the Postdoctoral Science Foundation Project of China [grant number 2015M580826]; the Natural Science Foundation Project of Shannxi [grant number 2016JQ1020]. J. Peng was supported partially by National Natural Science Foundation of China [grant number 11131006], [grant number 41390454].