Singularity Formation for the Multi-dimensional Compressible Degenerate Navier-Stokes Equations

被引：1

作者：

Huang, Yucong ^{[1
]}

Wang, Qin ^{[2
]}

Zhu, Shengguo ^{[3
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

[2] Yunnan Univ, Sch Math, Kunming 650091, Yunnan, Peoples R China

[3] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2023年 / 35卷 / 02期

基金：

英国工程与自然科学研究理事会; 中国国家自然科学基金;

关键词：

Compressible Navier-Stokes; Isentropic; Multi-dimensions; Vacuum; Degenerate viscosity; Classical solutions; Finite time blow-up; GLOBAL WEAK SOLUTIONS; SHALLOW-WATER EQUATIONS; CLASSICAL-SOLUTIONS; VISCOSITIES; DERIVATION; EXISTENCE;

D O I：

10.1007/s10884-021-10038-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the multi-dimensional (M-D) isentropic compressible Navier-Stokes equations with degenerate viscosities (ICNS) is considered in the whole space. We show that for a certain class of initial data with local vacuum, the regular solution of the corresponding Cauchy problem will blow up in finite time, no matter how small and smooth the initial data are. It is worth pointing out that local existence of regular solution considered in this paper has been established.

引用

页码：1769 / 1783

页数：15

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