Asymptotic stability of superposition of stationary solutions and rarefaction waves for 1D Navier–Stokes/Allen–Cahn system

2019 ◽  
Vol 266 (11) ◽  
pp. 7291-7326 ◽  
Author(s):  
Haiyan Yin ◽  
Changjiang Zhu
Keyword(s):  
Asymptotic Stability ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Rarefaction Waves

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.

Asymptotic stability of stationary Navier–Stokes flow in Besov spaces

2021 ◽  
pp. 1-22
Author(s):  
Jayson Cunanan ◽  
Takahiro Okabe ◽  
Yohei Tsutsui
Keyword(s):  
Asymptotic Stability ◽  
Stokes Flow ◽  
Besov Spaces ◽  
Stokes Equations ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Main Ingredient ◽  
Navier Stokes Equations ◽  
Whole Space

We discuss the asymptotic stability of stationary solutions to the incompressible Navier–Stokes equations on the whole space in Besov spaces. A critical estimate for the semigroup generated by the Laplacian with a perturbation is the main ingredient of the argument.

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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