变粘可压缩轴对称 Navier-Stokes 方程组全局强解的存在性

摘要/Abstract

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 $\Omega=\{(r,z)\vert r=\sqrt{x^2+y^2},(x,y,z)\in\mathbb{R}^3,r\in I\subset(0,+\infty),z\in(-\infty,+\infty)\}$. 当 $z\rightarrow\pm\infty$ 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.

关键词: Navier-Stokes 方程组, 轴对称, 粘性依赖密度, 强解

Abstract:

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 domain $\Omega=\{(r,z)\vert r=\sqrt{x^2+y^2},(x,y,z)\in\mathbb{R}^3,r\in I\subset(0,+\infty),z\in(-\infty,+\infty)\}$. When $z\rightarrow\pm\infty$, 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.

Key words: Navier-Stokes equations, Axisymmetric, Density-dependent, Strong solution

中图分类号:

0175.23

龚思梦, 张学耀, 郭真华. 变粘可压缩轴对称 Navier-Stokes 方程组全局强解的存在性[J]. 数学物理学报, 2024, 44(6): 1445-1475.

Gong Simeng, Zhang Xueyao, Guo Zhenhua. The Existence of Global Strong Solution to the Compressible Axisymmetric Navier-Stokes Equations with Density-Dependent Viscosities[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1445-1475.

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