On blowup phenomena of solutions to the Euler equations for Chaplygin gases

Huang, Shoujun; Wang, Rong

doi:10.1016/j.amc.2012.10.026

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…For system () with a = 0 and pressure (), the Ge and Sheng 5 considered the two‐dimensional gas expansion problem and proved the global existence of solutions to the expansion problem of a wedge of gas into vacuum with the half angel θ ∈ (0, π /2) for the generalized Chaplygin gas after obtaining some prior estimates. Subsequently, Cheung 6 investigated the solutions of the same system in general N dimension by starting with the following velocity form.

u false(t, boldx false) = c false(t false) false| boldx {false|}^{α - 1} boldx .

…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Global existence of the three‐dimensional compressible Euler equations for generalized Chaplygin gas with damping

Cheung

2020

Math Meth Appl Sci

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In this paper, we establish a global existence (GE) result for the threedimensional compressible Euler equations (CEE) for generalized Chaplygin gas (GCG) with damping. More precisely, by transforming the three-dimensional CEE for GCG with damping to a symmetric hyperbolic system, one shows that the total energy in H 3 is strictly decaying with time for any sufficiently small initial data. As a result, the GE result follows from the local well-posedness of the system in H 3. This gives the first GE result relating to the three-dimensional CEE.

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u false(t, boldx false) = c false(t false) false| boldx {false|}^{α - 1} boldx .

…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Global existence of the three‐dimensional compressible Euler equations for generalized Chaplygin gas with damping

Cheung

2020

Math Meth Appl Sci

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“…Such effects have always been paid a great deal of attention both because of their mathematical beauty [3,4,5] and practical applications [6]. The tendency of studying such phenomena is remaining nowadays as well, see, for example [7], where the case of Chaplygin gases is considered, [8,9], where the authors discuss weak shock waves, which is actually the case considered in the present paper, and also it is worth mentioning [10,11], where the influence of turbulence on detonations is investigated. The properties of global solvability for Euler equations and singularities of their solutions were also studied in a series of works [12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Singularities in one-dimensional Euler flows

Roop

2021

Preprint

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In this paper, a system of one-dimensional gas dynamics equations is considered. This system is a particular case of Jacobi type systems and has a natural representation in terms of 2-forms on 0-jet space. We use this observation to find a new class of multivalued solutions for an arbitrary thermodynamic state model and discuss singularities of their projections to the space of independent variables for the case of an ideal gas. Caustics and discontinuity lines are found.

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“…Kong and Wang [6] proved the global existence of smooth solutions for two-dimensional Chaplygin gases when the initial data are a small perturbation of a constant state and the initial vorticity vanishes. Recently, Huang and Wang [7] proved the blowup phenomenon of spherical symmetric solutions of Chaplygin gases; for more results on compressible Euler equations, one can refer to [8][9][10][11], especially the work of Christodoulou and Miao [12] on the formation of shocks.…”

Section: Introductionmentioning

confidence: 99%