For more information about this meeting, contact Kris Jenssen, Jinchao Xu, Xiantao Li, Yuxi Zheng, Hope Shaffer.

Title: | Vanishing viscosity limit from the Navier-Stokes to the Euler equations and measure-valued solutions for scalar conservation laws |

Seminar: | Computational and Applied Mathematics Colloquium |

Speaker: | M. Perepelitsa, University of Houston |

Abstract: |

In the first part of the talk we will discuss the problem of
obtaining weak solutions of the Euler equations for an isentropic flow
of gas in the zero viscosity limit from the solutions of the
Navier-Stokes equations in one dimension. The problem will be
considered in the compensated compactness framework, that was
introduced for scalar conservation laws by L.~Tartar. This approach is
based on a concept of a measure-valued solution to a system of PDEs. A
measure-valued solution is a convenient way to describe the situation
when functions representing the solution can take multiple values at a
single space-time point $(t,x).$ In the second part of the talk we
will show that for a single conservation law there is a
complete existence/uniqueness theory for such solutions, and
the usual weak entropy solutions can be approximated by a suitable
sequence of smooth measure-valued solutions. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 10 / 14 / 2011 |

Time: | 03:35pm - 04:25pm |