Asymptotic Stability of Combination of Viscous Contact Wave with Rarefaction Waves for One-Dimensional Compressible Navier–Stokes System

2009 ◽  
Vol 197 (1) ◽  
pp. 89-116 ◽  
Author(s):  
Feimin Huang ◽  
Jing Li ◽  
Akitaka Matsumura
Keyword(s):  
Asymptotic Stability ◽  
Stokes System ◽  
Navier Stokes ◽  
Rarefaction Waves ◽  
One Dimensional ◽  
Contact Wave

scholarly journals Asymptotic stability of viscous contact wave and rarefaction waves for the system of heat-conductive ideal gas without viscosity

2019 ◽  
Vol 17 (02) ◽  
pp. 211-234 ◽  
Author(s):  
Lili Fan ◽  
Guiqiong Gong ◽  
Shaojun Tang
Keyword(s):  
Asymptotic Stability ◽  
Initial Perturbation ◽  
Ideal Gas ◽  
Euler System ◽  
Navier Stokes ◽  
Rarefaction Waves ◽  
One Dimensional ◽  
Wave Patterns ◽  
The Cauchy Problem ◽  
Contact Wave

This paper is concerned with the Cauchy problem of heat-conductive ideal gas without viscosity, where the far field states are prescribed. When the corresponding Riemann problem for the compressible Euler system has the solution consisting of a contact discontinuity and rarefaction waves, we show that if the strengths of the wave patterns and the initial perturbation are suitably small, the unique global-in-time solution exists and asymptotically tends to the corresponding composition of a viscous contact wave with rarefaction waves, which extended the results by Huang–Li–Matsumura [Asymptotic stability of combination of viscous contact wave with rarefaction waves for one-dimensional compressible Navier–Stokes system, Arch. Ration. Mech. Anal. 197 (2010) 89–116.], where they treated the viscous and heat-conductive ideal gas.

scholarly journals Asymptotic Stability of Landau Solutions to Navier–Stokes System

2011 ◽  
Vol 202 (1) ◽  
pp. 115-131 ◽  
Author(s):  
Grzegorz Karch ◽  
Dominika Pilarczyk
Keyword(s):  
Asymptotic Stability ◽  
Stokes System ◽  
Navier Stokes
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