### Abstract

A key issue in gas dynamics in two space dimensions is the regularity of solutions near a sonic curve. We build a large class of regular solutions with given boundary conditions on the sonic line. The modeling equation is the pressure gradient equation, which is the same as Euler system when the parameters of the gas are pushed to certain extreme. We use a novel set of coordinates, involving both the space–time and state variables, to split regular terms from singular terms in the analysis.

Original language | English (US) |
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Pages (from-to) | 39-56 |

Number of pages | 18 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 443 |

Issue number | 1 |

DOIs | |

State | Published - Nov 1 2016 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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*Journal of Mathematical Analysis and Applications*, vol. 443, no. 1, pp. 39-56. https://doi.org/10.1016/j.jmaa.2016.04.002

**The structure of solutions near a sonic line in gas dynamics via the pressure gradient equation.** / Zhang, Tianyou; Zheng, Yuxi.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The structure of solutions near a sonic line in gas dynamics via the pressure gradient equation

AU - Zhang, Tianyou

AU - Zheng, Yuxi

PY - 2016/11/1

Y1 - 2016/11/1

N2 - A key issue in gas dynamics in two space dimensions is the regularity of solutions near a sonic curve. We build a large class of regular solutions with given boundary conditions on the sonic line. The modeling equation is the pressure gradient equation, which is the same as Euler system when the parameters of the gas are pushed to certain extreme. We use a novel set of coordinates, involving both the space–time and state variables, to split regular terms from singular terms in the analysis.

AB - A key issue in gas dynamics in two space dimensions is the regularity of solutions near a sonic curve. We build a large class of regular solutions with given boundary conditions on the sonic line. The modeling equation is the pressure gradient equation, which is the same as Euler system when the parameters of the gas are pushed to certain extreme. We use a novel set of coordinates, involving both the space–time and state variables, to split regular terms from singular terms in the analysis.

UR - http://www.scopus.com/inward/record.url?scp=84967158544&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84967158544&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2016.04.002

DO - 10.1016/j.jmaa.2016.04.002

M3 - Article

AN - SCOPUS:84967158544

VL - 443

SP - 39

EP - 56

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -