We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous...We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.展开更多
We investigate the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional compressible Navier-Stokes type system for a viscous,compressible,radiative and reactive gas,w...We investigate the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional compressible Navier-Stokes type system for a viscous,compressible,radiative and reactive gas,where the constitutive relations for the pressure p,the speci c internal energy e,the speci c volume v,the absolute temperature θ,and the specific entropy s are given by p=Rθv+aθ^(4)/3,e=C_(v)θ+avθ^(4),and s=C_(v)lnθ+4avθ^(3)/3+Rln v with R>0,C_(v)>0 and a>0 being the perfect gas constant,the speci c heat and the radiation constant,respectively.For such a specific gas motion,a somewhat surprising fact is that,generally speaking,the pressure p(v,s)is not a convex function of the specific volume v and the specific entropy s.Even so,we show in this paper that the rarefaction waves are time-asymptotically stable for large initial perturbation provided that the radiation constant a and the strength of the rarefaction waves are sufficiently small.The key point in our analysis is to deduce the positive lower and upper bounds on the specific volume and the absolute temperature,which are uniform with respect to the space and the time variables,but are independent of the radiation constant a.展开更多
文摘We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.
基金supported by the Fundamental Research Funds for the Central Universities and National Natural Science Foundation of China(Grant Nos.11731008 and 11671309)supported by the Fundamental Research Funds for the Central Universities(Grant No.YJ201962)supported by National Postdoctoral Program for Innovative Talents of China(Grant No.BX20180054).
文摘We investigate the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional compressible Navier-Stokes type system for a viscous,compressible,radiative and reactive gas,where the constitutive relations for the pressure p,the speci c internal energy e,the speci c volume v,the absolute temperature θ,and the specific entropy s are given by p=Rθv+aθ^(4)/3,e=C_(v)θ+avθ^(4),and s=C_(v)lnθ+4avθ^(3)/3+Rln v with R>0,C_(v)>0 and a>0 being the perfect gas constant,the speci c heat and the radiation constant,respectively.For such a specific gas motion,a somewhat surprising fact is that,generally speaking,the pressure p(v,s)is not a convex function of the specific volume v and the specific entropy s.Even so,we show in this paper that the rarefaction waves are time-asymptotically stable for large initial perturbation provided that the radiation constant a and the strength of the rarefaction waves are sufficiently small.The key point in our analysis is to deduce the positive lower and upper bounds on the specific volume and the absolute temperature,which are uniform with respect to the space and the time variables,but are independent of the radiation constant a.
