变粘可压缩轴对称Navier-Stokes方程组全局强解的存在性  

The Existence of Global Strong Solution to the Compressible Axisymmetric Navier-Stokes Equations with Density-Dependent Viscosities

作　　者：龚思梦 张学耀 郭真华 Gong Simeng;Zhang Xueyao;Guo Zhenhua(School of Mathematics and CNS,Northwest University,Xi'an 710127;School of Mathematics and Information Science,Guangxi University,Nan'ning 530004)

机构地区：[1]西北大学数学学院,非线性科学研究中心,西安710127 [2]广西大学数学与信息科学学院,南宁530004

出　　处：《数学物理学报（A辑）》2024年第6期1445-1475,共31页Acta Mathematica Scientia

基　　金：国家自然科学基金(11931013);广西自然科学基金(2022GXNSFDA035078)。

摘　　要：该文考虑三维空间中粘性依赖密度的可压缩Navier-Stokes方程组,得到了具有小能量大振荡初值的全局轴对称强解的存在唯一性,其中流体区域为周期域Ω={(r,z)|r=√x^(2)+y^(2),(x,y,z)∈R^(3),r∈I⊂(0,+∞),z∈(−∞,+∞)}.当z→±∞时,初始密度保持非真空状态.结果还表明,只要初始密度远离真空,解在任何时间内都不会发展成真空状态;并且该文给出了解的精确的衰减速率.In this paper,we consider the compressible Navier-Stokes equations with viscous-dependent density in 3D space,and obtain a global axisymmetric strong solution with small energy and large initial oscillations in a periodic domainΩ={(r,z)|r=√x^(2)+y^(2),(x,y,z)∈R^(3),r∈I⊂(0,+∞),z∈(−∞,+∞)}.When z→±∞,the initial density remains in a non-vacuum state.The results also show that as long as the initial density is far away from the vacuum,the solution will not develop the vacuum state in any time.And the exact decay rates of the solution is obtained.

关 键 词：NAVIER-STOKES 方程组 轴对称 粘性依赖密度 强解 

分 类 号：O175.23[理学—数学]