Stability of stationary solutions to the outflow problem for full compressible Navier-Stokes equations with large initial perturbation

Abstract

We investigate the large-time behavior of solutions to an outflow problem of the full compressible Navier-Stokes equations in the half line. The non-degenerate stationary solution is shown to be asymptotically stable under large initial perturbation with no restriction on the adiabatic exponent $\gamma$, provided that the boundary strength is sufficiently small. The proofs are based on the standard energy method and the crucial step is to obtain positive lower and upper bounds of the density and the temperature uniformly in time and space.

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References in corpus (2)

• Some Uniform Estimates and Large-Time Behavior for One-Dimensional Compressible Navier-Stokes System in Unbounded Domains with Large Data
• Inflow Problem for the One-dimensional Compressible Navier-Stokes Equations under Large Initial Perturbation

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• Asymptotic stability of wave patterns to compressible viscous and heat-conducting gases in the half space
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• Existence and Nonlinear Stability of Steady-States to Outflow Problem for the Full Two-Phase Flow
• Stability of degenerate stationary solution to the outflow problem for full Navier-Stokes equations