Vanishing viscosity limit for Navier–Stokes equations with general viscosity to Euler equations

Abstract

In this paper, we study vanishing viscosity limit of 1-D isentropic compressible Navier–Stokes equations with general viscosity to isentropic Euler equations. Firstly, we improve estimates of the entropy flux, then we obtain that the weak solution of the isentropic Euler equations is the inviscid limit of the isentropic compressible Navier–Stokes equations with general viscosity using the compensated compactness frame recently established by G.-Q. Chen and M. Perepelitsa.

Keywords:

• Navier–Stokes equations
• existence
• weak solutions
• compensated compactness
• general viscosity

AMS Subject Classifications:

• 35Q30
• 35L45
• 35L60
• 35L65
• 76N15

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by NSFC [grant number 11326160].