On Classical Solutions of the Compressible Euler Equations for Generalized Chaplygin Gas with Qualitative Analysis

被引：0

作者：

Cheung, Ka Luen ^{[1
]}

Wong, Sen ^{[1
]}

机构：

[1] Educ Univ Hong Kong, Dept Math & Informat Technol, Tai Po, 10 Lo Ping Rd, Hong Kong, Peoples R China

来源：

VIETNAM JOURNAL OF MATHEMATICS | 2023年

关键词：

Euler equations; Global-in-time; Generalized chaplygin gas; Finite-time blowup; Exact solutions; MOTION;

D O I：

10.1007/s10013-023-00651-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, exact classical solutions of the original three-dimensional compressible Euler equations for generalized Chaplygin gas are constructed by means of the ansatz of the fluid velocity u(t, x) = A' (t) A(-1()t) x. The qualitative analysis of a matrix ordinary differential equation reveals that the obtained exact solutions induce both unique smooth global-in-time and finite-time blowup exact solutions for given initial data. Moreover, the blowup mechanisms in the induced examples are discussed.

引用

页数：14

共 50 条

[31] Concentration Phenomenon of Riemann Solutions for the Relativistic Euler Equations with the Extended Chaplygin Gas
Zhang, Yunfeng
Sun, Meina
[J]. ACTA APPLICANDAE MATHEMATICAE, 2020, 170 (01) : 539 - 568
[32] Limits of Solutions to the Relativistic Euler Equations for Modified Chaplygin Gas by Flux Approximation
Yu Zhang
Hanchun Yang
[J]. Acta Applicandae Mathematicae, 2020, 169 : 1 - 32
[33] Limits of Solutions to the Relativistic Euler Equations for Modified Chaplygin Gas by Flux Approximation
Zhang, Yu
Yang, Hanchun
[J]. ACTA APPLICANDAE MATHEMATICAE, 2020, 169 (01) : 1 - 32
[34] Concentration Phenomenon of Riemann Solutions for the Relativistic Euler Equations with the Extended Chaplygin Gas
Yunfeng Zhang
Meina Sun
[J]. Acta Applicandae Mathematicae, 2020, 170 : 539 - 568
[35] RIEMANN PROBLEM FOR THE RELATIVISTIC GENERALIZED CHAPLYGIN EULER EQUATIONS
Huang, Meixiang
Shao, Zhiqiang
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2016, 15 (01) : 127 - 138
[36] Finite-time blowup of smooth solutions for the relativistic generalized Chaplygin Euler equations
Cheung, Ka Luen
Wong, Sen
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 489 (02)
[37] The transition of Riemann solutions of the modified Chaplygin gas equations with friction to the solutions of the Chaplygin gas equations
Guo, Lihui
Li, Tong
Yin, Gan
[J]. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2022, 102 (03):
[38] Classical solutions for the Euler equations of compressible fluid dynamics: A new topological approach
Boureni, Dalila
Georgiev, Svetlin
Kheloufi, Arezki
Mebarki, Karima
[J]. APPLIED GENERAL TOPOLOGY, 2022, 23 (02): : 463 - 480
[39] Entropy solutions of the compressible Euler equations
Magnus Svärd
[J]. BIT Numerical Mathematics, 2016, 56 : 1479 - 1496
[40] Classical Solutions for 1D Compressible Euler Equations with Over Damping
Liu, Jianli
Wang, Jingwei
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2022, 24 (03)

← 1 2 3 4 5 →