输运系数依赖温度的可压缩辐射流体解的整体存在性  

Global Existence of the Compressible and Radiative Flux with Temperature-Dependent Transport Coefficients

作　　者：张明玉 Zhang Mingyu(School of Mathematics and Information Science,Weifang University,Shandong Weifang 261061)

机构地区：[1]潍坊学院数学与信息科学学院,山东潍坊261061

出　　处：《数学物理学报（A辑）》2023年第2期458-480,共23页Acta Mathematica Scientia

基　　金：山东省自然科学基金(ZR2021QA049)。

摘　　要：该文主要研究了当粘性系数λ和热传导系数κ依赖于温度θ,即λ(θ)=θ^(α),κ(θ)=1+θ^(β),其中α∈[0,+∞),β∈(2,+∞)时,带有辐射项的可压缩Navier-Stokes方程解的全局存在性和非线性稳定性.在关于参数α和初值的某些假设下,该文得到了强解的全局存在唯一性.此外,在基于时间的一直估计下,本文还证明了解的非线性指数稳定性.需要指出的是,如果α较小,并且增长指数β任意大,则初值可以任意大.In this paper,we are concerned with the the global existence and non-linear stability of the compressible and radiative Navier-Stokes equations when the viscosity入and heat conductivity k depend on temperature θ,i.e.,λ(θ)=θ^(α),κ(θ)=1+θ^(β) with α∈[0,+∞),β∈(2,+∞).The global existence and uniqueness of strong solutions are obtained under the assumptions on the parameter a and initial data.In addition,we also proved the non-linear exponential stability of the solutions on the basis of the fundamental uniform-in-time estimates.It should be note that the initial data could be large if α is small and the growth exponent θ can be arbitrarily large.

关 键 词：可压缩NAVIER-STOKES方程 热辐射 输运系数依赖温度 大初值 整体解 

分 类 号：O175.27[理学—数学]