# Meeting Details

For more information about this meeting, contact Kris Jenssen, Victor Nistor, 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 Computational and Applied Mathematics Colloquium M. Perepelitsa, University of Houston 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 10 / 14 / 2011 03:35pm - 04:25pm