Global existence and asymptotic behavior of solutions to a free boundary problem for the 1D viscous radiative and reactive gas
type: Item
instance of: scholarly article
title: Global existence and asymptotic behavior of solutions to a free boundary problem for the 1D viscous radiative and reactive gas
zbMATH Open document ID: 1397.35180
author: Chang Ming Song
author: Hong Li
author: Jianlin Zhang
publication date: 2018-06-07T00:00:00Z
review text: This paper is concerning a free-boundary problem for the compressible Navier-Stokes system which describes the 1D-flows of a viscous heat-conducting radiative and reactive gas, with no restrictions on the size of initial data. The Stefan-Boltzmann radiative law is considered for pressure and internal energy. The temperature appear both in a ``perfect polytropic contribution and a fourth-order radiative part'' in the state equation (1.3), quite similar with the relation (1.16) given in [\textit{B. Ducomet} and \textit{A. Zlotnik}, Arch. Ration. Mech. Anal. 177, No. 2, 185--229 (2005; Zbl 1070.76044)], where is specified that `` this model can be shown to model correctly some astrophysical situations of interest like stellar evolution or interstellar medium dynamics''. The new element of the paper is to remove some restrictions on the specific volume, imposed in previous works. With some assumptions on the heat conductivity, the existence of a unique global solution is proved, in Sobolev spaces \(H^2\) and \(H^4\) (for reactant mass fraction). The point is to obtain uniform positive lower and upper bounds for the specific volume. For this, some important estimates given in [\textit{J. Jiang} and \textit{S. Zheng}, J. Math. Phys. 53, No. 12, 123704, 33 p. (2012; Zbl 1331.35401)] are used or adapted for the present assumptions. The time-asymptotic limits of the global solutions are also obtained. The main tools are Sobolev's, Holder's and Gronwall's inequalities, embedding theorems, interpolation inequality and Poincaré's inequality. A large list of references is given in the last part.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35D35
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 6881939
zbMATH Keywords: radiative and reactive gases
zbMATH Keywords: global solutions
zbMATH Keywords: free-boundary problems
zbMATH Keywords: asymptotic behavior
reviewed by: Gelu Paşa
MaRDI profile type: Publication
full work available at URL: s10114-017-7316-7
OpenAlex ID: W2775137421
cites work: Global Solutions to the Compressible Navier–Stokes Equations for a Reacting Mixture
cites work: Global solutions of the compressible navier-stokes equations with larger discontinuous initial data
cites work: Global solutions to a model for exothermically reacting, compressible flows with large discontinuous initial data
cites work: Q5465390
cites work: On the motion of a viscous compressible radiative-reacting gas
cites work: A multidimensional model for the combustion of compressible fluids
cites work: On the stability of stellar structure in one dimension II : the reactive case
cites work: Q4704601
cites work: Q4502721
cites work: On the dynamics of gaseous stars
cites work: The equations of magnetohydrodynamics: on the interaction between matter and radiation in the evolution of gaseous stars
cites work: Stabilization for viscous compressible heat-conducting media equations with nonmonotone state functions.
cites work: Lyapunov functional method for 1D radiative and reactive viscous gas dynamics
cites work: On the large-time behavior of 1D radiative and reactive viscous flows for higher-order kinetics
cites work: Q5702675
cites work: Singular limits in thermodynamics of viscous fluids
cites work: Multicomponent reactive flows: global-in-time existence for large data
cites work: Asymptotic behavior of the solution to the system for a viscous reactive gas
cites work: Lagrange structure and dynamics for solutions to the spherically symmetric compressible Navier-Stokes equations
cites work: Q4695270
cites work: Large-time behaviour of solutions for the outer pressure problem of a viscous heat-conductive one-dimensional real gas
cites work: On initial boundary value problems for a viscous, heat-conducting, one- dimensional real gas
cites work: On the asymptotic behavior of the motion of a viscous, heat-conducting, one-dimensional real gas
cites work: Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain
cites work: On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations
cites work: Global solvability and asymptotic behavior of a free boundary problem for the one-dimensional viscous radiative and reactive gas
cites work: Global well-posedness and exponential stability of solutions for the viscous radiative and reactive gas
cites work: Global existence of large solutions to initial boundary value problems for a viscous, heat-conducting, one-dimensional real gas
cites work: Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas
cites work: On the outer pressure problem of the one-dimensional polytropic ideal gas
cites work: On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with stress-free condition
cites work: Nonlinear parabolic-hyperbolic coupled systems and their attractors
cites work: Exponential stability for a nonlinear one-dimensional heat-conductive viscous real gas
cites work: Universal attractor in \(H^4\) for the nonlinear one-dimensional compressible Navier-Stokes equations
cites work: Global smooth solutions for 1D thermally radiative magnetohydrodynamics
cites work: Global smooth solutions for the compressible viscous and heat-conductive gas
cites work: Remarks on global smooth solutions to a 1D self-gravitating viscous radiative and reactive gas
cites work: Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems
cites work: Global existence and exponential stability of spherically symmetric solutions to a compressible combustion radiative and reactive gas
cites work: On The Coupled Cahn-hilliard Equations
cites work: On the first initial-boundary value problem of compressible viscous fluid motion
cites work: On the free boundary value problem for compressible viscous fluid motion
cites work: Global solution to the one-dimensional equations for a self-gravitating viscous radiative and reactive gas
cites work: TEMPORALLY GLOBAL SOLUTION TO THE EQUATIONS FOR A SPHERICALLY SYMMETRIC VISCOUS RADIATIVE AND REACTIVE GAS OVER THE RIGID CORE
cites work: Global solution for the mixture of real compressible reacting flows in combustion
cites work: VACUUM STATE FOR SPHERICALLY SYMMETRIC SOLUTIONS OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS
cites work: Remarks on global existence and exponential stability of solutions for the viscous radiative and reactive gas with large initial data
cites work: Global solution for a one-dimensional model problem in thermally radiative magnetohydrodynamics
cites work: Universal attractors for the Navier-Stokes equations of compressible and heat-conductive fluid in bounded annular domains in \(\mathbb{R}^n\)
DOI: 10.1007/S10114-017-7316-7
Recommended article: Asymptotics for 1D flows with time-dependent external fields
Recommended article: One-dimensional viscous radiative gas with temperature dependent viscosity
Recommended article: Cauchy problem of the one-dimensional compressible viscous radiative and reactive gas with degenerate density dependent viscosity
Recommended article: Large-time behavior of the motion of a viscous heat-conducting one-dimensional gas coupled to radiation
Recommended article: Global solutions to one-dimensional equations for a self-gravitating viscous radiative and reactive gas with density-dependent viscosity
Recommended article: Global Regularity for a Radiation Hydrodynamics Model with Viscosity and Thermal Conductivity

Global existence and asymptotic behavior of solutions to a free boundary problem for the 1D viscous radiative and reactive gas (Recommended article)
Recommended article: Global spherically symmetric flows for a viscous radiative and reactive gas in an exterior domain
Similarity Score: 0.8202737
Recommender Run: Recommender Run 2

Global existence and asymptotic behavior of solutions to a free boundary problem for the 1D viscous radiative and reactive gas (Recommended article)
Recommended article: The outflow problem for the radiative and reactive gas: existence, stability and convergence rate
Similarity Score: 0.81147677
Recommender Run: Recommender Run 2

Global existence and asymptotic behavior of solutions to a free boundary problem for the 1D viscous radiative and reactive gas (Recommended article)
Recommended article: ASYMPTOTIC BEHAVIOR OF THE MOTION OF A VISCOUS HEAT-CONDUCTING ONE-DIMENSIONAL GAS WITH RADIATION: THE PURE SCATTERING CASE
Similarity Score: 0.8113252
Recommender Run: Recommender Run 2

Global existence and asymptotic behavior of solutions to a free boundary problem for the 1D viscous radiative and reactive gas (Recommended article)
Recommended article: Q3632302
Similarity Score: 0.8109327
Recommender Run: Recommender Run 2

Global existence and asymptotic behavior of solutions to a free boundary problem for the 1D viscous radiative and reactive gas (published in)
published in: Acta Mathematica Sinica, English Series