Czechoslovak Mathematical Journal, first online, pp. 1-24


Vanishing viscosity of one-dimensional isentropic Navier-Stokes equations with density dependent viscous coefficient

Meiying Cui

Received July 13, 2022.   Published online February 24, 2025.

Abstract:  We study the vanishing viscosity of isentropic compressible Navier-Stokes equations with density dependent viscous coefficient in the presence of shock wave. Given a shock wave to the corresponding Euler equations, we can construct a sequence of solutions to one-dimensional compressible isentropic Navier-Stokes equations which converge to the shock wave as the viscosity tends to zero. The proof is given by an elementary energy method.
Keywords:  vanishing viscosity limit; compressible isentropic Navier-Stokes equation; Euler equation; shock wave
Classification MSC:  35Q30, 76N06

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Affiliations:   Meiying Cui, School of Mathematics and Statistics, Yulin University, Yulin, 719000, P. R. China and School of Mathematics and CNS, Northwest University, No. 1 Xuefu Avenue, Chang'an District, Xi'an 710069, P. R. China, e-mail: mycui2004@163.com


 
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