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Nonlinear stability of rarefaction waves for a viscous radiative and reactive gas with large initial perturbation

Science China Mathematics 2021年第12期64卷 2637-2666页

作者： Guiqiong Gong Lin He Yongkai Liao School of Mathematics and Statistics Wuhan UniversityWuhan 430072China Hubei Key Laboratory of Computational Science Wuhan UniversityWuhan 430072China College of Mathematics Sichuan UniversityChengdu 610064China Institute of Applied Physics and Computational Mathematics Beijing 100088China

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.

关键词： viscous radiative and reactive gas rarefaction waves nonlinear stability large initial perturbation

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NONLINEAR STABILITY OF VISCOUS SHOCK WAVES FOR ONE-DIMENSIONAL NONISENTROPIC COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH A CLASS OF large initial perturbation

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Acta Mathematica Scientia 2018年第3期38卷 973-1000页

作者：唐少君张澜 School of Mathematics and Statistics Wuhan University

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.

关键词： One-dimensional nonisentropic compressible Navier–Stokes equations viscous shock waves nonlinear stability large initial perturbation

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