For more information about this meeting, contact Tianyou Zhang, Stephanie Zerby.

Title: | Existence of a classical supersonic solutions at a sonic line for the steady Euler equations (II) |

Seminar: | Hyperbolic and Mixed Type PDEs Seminar |

Speaker: | Tianyou Zhang, Penn State |

Abstract: |

Given a smooth curve as a sonic line in the plane, we construct a classical smooth supersonic solution on one side of the curve for the steady compressible Euler system of equations in two space dimensions. We allow the location of the given sonic curve to be arbitrary, but the interior normal derivative of the speed of sound on the curve is assumed to be negative in the direction toward the supersonic domain. Our construction hinges on a new set of coordinates introduced here to handle the inherent degeneracy of the system at the sonic curve. The solutions are established near by the sonic curve only, as shock waves are unavoidable a short distance away from the curve. The streamlines of the solutions are analyzed to show that the shock-free portion of the solutions may be combined with known results of existence of subsonic solutions on the other side of the curve to form shock-free transonic flows in a channel for the steady Euler system. Hence, the current result is a generalization of the classical exact solution of Ringleb toward a more general existence. |

### Room Reservation Information

Room Number: | MB216 |

Date: | 09 / 13 / 2012 |

Time: | 10:00am - 10:50am |