### Abstract

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 ρu_{t} + p_{x} = 0, ρυ_{t} + p_{y} = 0, ρE_{t} + (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(u^{2} + υ^{2}) + 1/γ-1 p/ρ is the energy. The natural (parabolically degenerate) boundary value is used.

Original language | English (US) |
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Pages (from-to) | 1849-1868 |

Number of pages | 20 |

Journal | Communications in Partial Differential Equations |

Volume | 22 |

Issue number | 11-12 |

State | Published - Dec 1 1997 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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*Communications in Partial Differential Equations*, vol. 22, no. 11-12, pp. 1849-1868.

**Existence of solutions to the transonic pressure-gradient equations of the compressible Euler equations in elliptic regions.** / Zheng, Yuxi.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Zheng, Yuxi

PY - 1997/12/1

Y1 - 1997/12/1

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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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 -