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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. $$ufalse(t,\mathrm{boldx}false)=cfalse(tfalse)false|\mathrm{boldx}{false|}^{\alpha -1}\mathrm{boldx}.$$ …”

confidence: 99%

“…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. $$ufalse(t,\mathrm{boldx}false)=cfalse(tfalse)false|\mathrm{boldx}{false|}^{\alpha -1}\mathrm{boldx}.$$ …”

confidence: 99%

“…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].…”

confidence: 99%

“…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.…”

confidence: 99%