TY - JOUR

T1 - Existence of solutions to the transonic pressure-gradient equations of the compressible Euler equations in elliptic regions

AU - Zheng, Yuxi

N1 - Funding Information:
The author wishes to thank L. C. Evans, Taiping Liu, and Tong Zhang for stimulating discussions and suggestions. The author also wishes to thank a referee for his/her questions on an earlier presentation of the appendix and for calling his attention to a couple of references. This work is supported in part by NSF DMS-9303414 and an Alfred P. Sloan Research Fellows award.

PY - 1997

Y1 - 1997

N2 - We establish the existence of a smooth solution in its elliptic region in the self-similar plane to the pressure-gradient system arisen from the wave-particle splitting of the two-dimensional compressible Euler system of equations. The pressure-gradient system takes the form ρut + px = 0, ρυt + py = 0, ρEt + (up)x + (υp)y = 0. Here (u, υ) is the velocity, ρ is the density which is independent of time resulted from the splitting procedure, p is the pressure, and E = 1/2(u2 + υ2) + 1/γ-1 p/ρ is the energy. The natural (parabolically degenerate) boundary value is used.

AB - We establish the existence of a smooth solution in its elliptic region in the self-similar plane to the pressure-gradient system arisen from the wave-particle splitting of the two-dimensional compressible Euler system of equations. The pressure-gradient system takes the form ρut + px = 0, ρυt + py = 0, ρEt + (up)x + (υp)y = 0. Here (u, υ) is the velocity, ρ is the density which is independent of time resulted from the splitting procedure, p is the pressure, and E = 1/2(u2 + υ2) + 1/γ-1 p/ρ is the energy. The natural (parabolically degenerate) boundary value is used.

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U2 - 10.1080/03605309708821323

DO - 10.1080/03605309708821323

M3 - Article

AN - SCOPUS:0000277304

VL - 22

SP - 1849

EP - 1868

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 11-12

ER -