Existence of global strong solution to Cauchy problem for one-dimensional barotropic compressible Navier–Stokes equations

Abstract

In this paper, we study the Cauchy problem for 1D barotropic compressible Navier–Stokes equations with density-dependent viscosity. The viscosity coefficient is proportional to with , where is the density. Under certain assumptions imposed on the initial data, we obtain the global existence, uniqueness, and regularity of the strong solution. Some ideas and more delicate estimates are introduced to prove these results.

Keywords:

• Navier–Stokes equations
• Cauchy problem
• strong solution

AMS Subject Classifications:

• 35Q35; 76D03

Notes

The research of R.X. Lian is supported by NNSFC [grant number 11101145], China Postdoctoral Science Foundation [grant number 2012M520360], Doctoral Foundation of North China University of Water Sources and Electric Power [grant number 201032], and Innovation Scientists and Technicians Troop Construction Projects of Henan Province. The research of J. Liu is supported by NNSFC [grant number 11326140] and the Doctoral Starting up Foundation of QuZhou University [grant number BSYJ201314].

Both authors contributed to each part of this work equally.