Zero-viscosity–capillarity limit toward rarefaction wave with vacuum for the Navier–Stokes–Korteweg equations of compressible fluids

2020 ◽  
Vol 61 (11) ◽  
pp. 111501
Author(s):  
Yeping Li ◽  
Peicheng Zhu
Keyword(s):  
Rarefaction Wave ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Zero Viscosity

FLOWS OF VISCOUS COMPRESSIBLE FLUIDS UNDER STRONG STRATIFICATION: INCOMPRESSIBLE LIMITS FOR LONG-RANGE POTENTIAL FORCES

2011 ◽  
Vol 21 (01) ◽  
pp. 7-27 ◽  
Author(s):  
EDUARD FEIREISL
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Stokes System ◽  
Hybrid Methods ◽  
Singular Limit ◽  
Acoustic Energy ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Whole Space ◽  
Rage Theorem

We study the singular limit of the compressible Navier–Stokes system in the whole space ℝ3, where the Mach number and Froude number are proportional to a small parameter ε → 0. The central issue is the local decay of the acoustic energy proved by means of the RAGE theorem. The result is quite general and the proposed approach can be applied to a large variety of problems that concern propagation of acoustic waves in compressible fluids. In particular, the method can be used for showing stability of various numerical schemes based on the so-called hybrid methods.

Stability of the rarefaction wave for a coupled compressible Navier-Stokes/Allen-Cahn system

2018 ◽  
Vol 41 (12) ◽  
pp. 4724-4736 ◽  
Author(s):  
Ting Luo ◽  
Haiyan Yin ◽  
Changjiang Zhu
Keyword(s):  
Rarefaction Wave ◽  
Navier Stokes
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