scholarly journals Asymptotic Stability of the Superposition of Viscous Contact Wave with Rarefaction Waves for the Compressible Navier--Stokes--Maxwell Equations

2021 ◽  
Vol 53 (5) ◽  
pp. 6122-6163
Author(s):  
Huancheng Yao ◽  
Changjiang Zhu
Keyword(s):  
Asymptotic Stability ◽  
Maxwell Equations ◽  
Navier Stokes ◽  
Rarefaction Waves ◽  
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.

Stability of the composite wave for compressible Navier–Stokes/Allen–Cahn system

2019 ◽  
Vol 30 (02) ◽  
pp. 343-385
Author(s):  
Ting Luo ◽  
Haiyan Yin ◽  
Changjiang Zhu
Keyword(s):  
Cauchy Problem ◽  
Large Time ◽  
Large Time Behavior ◽  
Navier Stokes ◽  
Time Behavior ◽  
Rarefaction Waves ◽  
Small Perturbations ◽  
The Cauchy Problem ◽  
Composite Wave ◽  
Contact Wave

This paper is devoted to the study of the nonlinear stability of the composite wave consisting of two rarefaction waves and a viscous contact wave for the Cauchy problem to a one-dimensional compressible non-isentropic Navier–Stokes/Allen–Cahn system which is a combination of the classical Navier–Stokes system with an Allen–Cahn phase field description. We first construct the composite wave through Euler equations under the assumption of [Formula: see text] for the large time behavior, and then prove that the composite wave is time asymptotically stable under small perturbations for the corresponding Cauchy problem of the non-isentropic Navier–Stokes/Allen–Cahn system. The proof is mainly based on a basic energy method.

scholarly journals The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wen-Juan Wang ◽  
Yan Jia
Keyword(s):  
Weak Solution ◽  
Asymptotic Stability ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Perturbed System ◽  
Regular Class ◽  
Stability Issue ◽  
The Stability

We study the stability issue of the generalized 3D Navier-Stokes equations. It is shown that if the weak solutionuof the Navier-Stokes equations lies in the regular class∇u∈Lp(0,∞;Bq,∞0(ℝ3)),(2α/p)+(3/q)=2α,2<q<∞,0<α<1, then every weak solutionv(x,t)of the perturbed system converges asymptotically tou(x,t)asvt-utL2→0,t→∞.

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