Finite-time singularity formation for the original multidimensional compressible Euler equations for generalized Chaplygin gas

Cheung, Ka Luen; Wong, Sen

doi:10.1007/s00033-020-1287-8

Cited by 4 publications

(3 citation statements)

References 20 publications

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“…where a is a positive constant, such that 0 < a < n. Obviously, we can obtain G 1 (0) ≥ 0 from inequality (17), which implies G 1 (t) ≥ 0 for t ∈ [0, T] and…”

Section: Integration Methods With Test Functionsmentioning

confidence: 98%

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Formation of Singularity for Isentropic Irrotational Compressible Euler Equations

Liu,

Qin,

Yuen

2024

Symmetry

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The domain of science and engineering relies heavily on an in-depth comprehension of fluid dynamics, given the prevalence of fluids such as water, air, and interstellar gas in the universe. Euler equations form the basis for the study of fluid motion. This paper is concerned with the Cauchy problem of isentropic compressible Euler equations away from the vacuum. We use the integration method with the general test function f=f(r), proving that there exist the corresponding blowup results of C1 irrotational solutions for Euler equations and Euler equations with time-dependent damping in Rn (n≥2), provided the density-independent initial functional is sufficiently large. We also provide two simple and explicit test functions f(r)=r and f(r)=1+r, to demonstrate the blowup phenomenon in the one-dimensional case. In particular, our results are applicable to the non-radial system.

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“…where a is a positive constant, such that 0 < a < n. Obviously, we can obtain G 1 (0) ≥ 0 from inequality (17), which implies G 1 (t) ≥ 0 for t ∈ [0, T] and…”

Section: Integration Methods With Test Functionsmentioning

confidence: 98%

“…Those interested can find more comprehensive studies on the blowup phenomena of Euler equations in [13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Formation of Singularity for Isentropic Irrotational Compressible Euler Equations

Liu,

Qin,

Yuen

2024

Symmetry

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show abstract

“…Moreover, the blowup of smooth solutions to the compressible Euler equations for Chaplygin gas was studied in [17,18]. For more results about the Chaplygin gas equation and the extended Chaplygin gas equation, we can refer to [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions to the Euler equations for Chaplygin gas

Jiang,

Dong

2024

Phys. Scr.

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In this paper, we study the analytical solutions to the Euler equations for Chaplygin gas. First, we construct two exact solutions for the one-dimensional system by using a self-similar ansatz. Second, we present some analytical solutions for the N-dimensional radially symmetric system. Third, we extend the above results to the two-phase flow case. The concentration and cavitation phenomena are observed from the constructed solutions.

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

Cheung,

Wong

2023

Vietnam J. Math.

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Finite-time singularity formation for the original multidimensional compressible Euler equations for generalized Chaplygin gas

Cited by 4 publications

References 20 publications

Formation of Singularity for Isentropic Irrotational Compressible Euler Equations

Formation of Singularity for Isentropic Irrotational Compressible Euler Equations

Analytical solutions to the Euler equations for Chaplygin gas

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

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