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 (I) |

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 / 11 / 2012 |

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