Stability of Stationary Solutions to the Inflow Problem for Full Compressible Navier--Stokes Equations with a Large Initial Perturbation

2017 ◽  
Vol 49 (3) ◽  
pp. 2138-2166 ◽  
Author(s):  
Hakho Hong ◽  
Teng Wang
Keyword(s):  
Stokes Equations ◽  
Initial Perturbation ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Inflow Problem ◽  
Large Initial Perturbation

OPTIMAL CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH POTENTIAL FORCES

2007 ◽  
Vol 17 (05) ◽  
pp. 737-758 ◽  
Author(s):  
RENJUN DUAN ◽  
SEIJI UKAI ◽  
TONG YANG ◽  
HUIJIANG ZHAO
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Initial Perturbation ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Potential Force ◽  
Navier Stokes Equations ◽  
Optimal Convergence ◽  
Whole Space ◽  
Optimal Convergence Rates

For the viscous and heat-conductive fluids governed by the compressible Navier–Stokes equations with an external potential force, there exist non-trivial stationary solutions with zero velocity. By combining the Lp - Lq estimates for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the stationary profile in the whole space when the initial perturbation of the stationary solution and the potential force are small in some Sobolev norms. More precisely, the optimal convergence rates of the solution and its first order derivatives in L2-norm are obtained when the L1-norm of the perturbation is bounded.

Converge rates towards stationary solutions for the outflow problem of planar magnetohydrodynamics on a half line

2019 ◽  
Vol 149 (5) ◽  
pp. 1291-1322 ◽  
Author(s):  
Haiyan Yin
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Weighted Sobolev Space ◽  
Initial Perturbation ◽  
Global Solutions ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Weighted Energy Method ◽  
The Relationship

AbstractIn this paper, convergence rates of solutions towards stationary solutions for the outflow problem of planar magnetohydrodynamics (MHD) are investigated. Inspired by the relationship between MHD and Navier-Stokes, we prove that the global solutions of the planar MHD converge to the corresponding stationary solutions of Navier-Stokes equations. We obtain the corresponding convergence rates based on the weighted energy method when the initial perturbation belongs to some weighted Sobolev space.

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