变粘可压缩轴对称 Navier-Stokes 方程组全局强解的存在性

Abstract

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

CLC Number:

0175.23

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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References 43

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

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