Some Uniform Estimates and Large-Time Behavior for One-Dimensional Compressible Navier-Stokes System in Unbounded Domains with Large Data

Abstract

This paper is concerned with the large-time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible Navier-Stokes system describing the one-dimensional motion of a viscous heat-conducting perfect polytropic gas in unbounded domains. The temperature is proved to be bounded from below and above independently of both time and space. Moreover, the global solution is showed to be asymptotically stable as time tends to infinity. Note that the initial data can be arbitrarily large. This result is proved by using elementary energy methods.

Cited by in corpus (26)

• One-Dimensional Compressible Heat-Conducting Gas with Temperature-Dependent Viscosity
• Global small solutions of heat conductive compressible Navier-Stokes equations with vacuum: smallness on scaling invariant quantity
• Stability of stationary solutions to the outflow problem for full compressible Navier-Stokes equations with large initial perturbation
• Asymptotic stability of wave patterns to compressible viscous and heat-conducting gases in the half space
• On one-dimensional compressible Navier-Stokes equations for a reacting mixture in unbounded domains
• Global well-posedness of non-heat conductive compressible Navier-Stokes equations in 1D
• Nonlinear stability of rarefaction waves for a viscous radiative and reactive gas with large initial perturbation
• The Cauchy Problem for Non-Isentropic compressible Navier-Stokes/Allen-Cahn system with Degenerate Heat-Conductivity
• Large-time behavior for spherically symmetric flow of viscous polytropic gas in exterior unbounded domain with large initial data
• On the Global Strong Solutions to Magnetohydrodynamics with Density-Dependent Viscosity and Degenerate Heat-Conductivity in Unbounded Domains
• Global well-posedness of the 1D compressible Navier-Stokes equations with constant heat conductivity and nonnegative density
• Entropy-bounded solutions to the compressible Navier-Stokes equations: with far field vacuum
• Entropy-bounded solutions to the one-dimensional heat conductive compressible Navier-Stokes equations with far field vacuum
• On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with degenerate heat conductivity
• Refined pointwise estimates for solutions to the 1D barotropic compressible Navier--Stokes equations: An application to the long-time behavior of a point mass
• Local existence and uniqueness of heat conductive compressible Navier-Stokes equations in the presence of vacuum and without initial compatibility conditions
• Global smooth solutions to the nonisothermal compressible fluid models of Korteweg type with large initial data
• Global weak solutions and long time behavior for 1D compressible MHD equations without resistivity
• Global Existence and Large-time Behavior of Solutions to the Cauchy Problem of One-dimensional Viscous Radiative and Reactive Gas
• On Global Classical Solutions to 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum
• Global Existence of Strong Solutions to Compressible Navier-Stokes System with Degenerate Heat Conductivity in Unbounded Domains
• Global Spherical Symmetric Flows for a Viscous Radiative and Reactive Gas in an Exterior Domain with Large Initial Data
• Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum
• Non-existence of global classical solutions to barotropic compressible Navier-Stokes equations with degenerate viscosity and vacuum
• Global existence of strong solutions to the planar compressible magnetohydrodynamic equations with large initial data in unbounded domains
• Propagation of uniform boundedness of entropy and inhomogeneous regularities for viscous and heat conductive gases with far field vacuum in three dimensions