Dr. Geng Chen: Large solutions of compressible Euler equations

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Venue:DM 193

Dr. Geng Chen from Georgia Institute of Technology will be on campus on Thursday, February 4, 2016. His talk is scheduled for 3:30 PM in DM 193. The title and abstract follow:

Title: Large solutions of compressible Euler equations.

Abstract: Compressible Euler equations (introduced by Euler in 1757) model the motion of compressible inviscid fluids such as gases. It is well-known that solutions of compressible Euler equations often develop discontinuities, i.e. shock waves. Successful theories have been established in the past 150 years for small solutions in one space dimension. The theory on large solutions is widely open for a long time, even in one space dimension. In this talk, I will discuss some recent exciting progresses in this direction. In first part of this talk, I will discuss our complete resolution of shock formation problem, which extends the celebrated work of Peter Lax on small solutions in 1964. Our breakthrough relies on the discovery of a sharp time-dependent lower bound on density, when solutions approach vacuum in infinite time. In the second part, I will show our recent negative example concerning the failure of current available frameworks on approximate solutions in order to establish large BV (bounded total variation) theory. The talk is based on my joint works with A. Bressan, H.K. Jenssen, R. Pan, R. Young, Q. Zhang, and S. Zhu.