一维线性Navier-Stokes-Fourier方程组解的逐点估计  

The Pointwise Estimates to Solutions for 1-dimensional Linear Navier-Stokes-Fourier Equations

作　　者：安正达 张琦[1] AN ZHENGDA;ZHANG QI(School of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China)

机构地区：[1]南京航空航天大学数学学院,南京211106

出　　处：《应用数学学报》2024年第2期269-283,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.NSFC11671193)资助项目。

摘　　要：在本文中,我们研究一维线性Navier-Stokes-Fourier方程组,在适当的初值条件下,给出了解的衰减性的逐点估计,并刻画了解的衰减方向,同时验证了广义的Huygens原理成立.为此,我们通过Fourier变换的方法,将方程组Green函数的Fourier变换划分为低频、中频、高频三部分,分别证明了相应频率段的Green函数的衰减性质,再通过Fourier逆变换与基本解的性质,得到原问题解的衰减估计.In this paper,we study the 1-dimensional linear Navier-Stokes-Fourier equations and obtain the pointwise estimates of the decay properties of the solution under the appropriate initial value conditions,and describe the decay direction of the solution,and verify that the generalized Huygens'principle holds.To this end,we divide the Fourier transform of the Green function of the equations into low-frequency,mid-frequency and high-frequency parts by means of Fourier transform,and prove the decay properties of the Green function in the corresponding frequency parts,and then obtain the decay estimates of the solutions by means of the Fourier inverse transform and the properties of the fundamental solutions.

关 键 词：Navier-Stokes-Fourier方程组 逐点估计 FOURIER变换 Huygens原理 GREEN函数 

分 类 号：O175.2[理学—数学]