Time
2021-03-23 09:00, 7 hours ago
Venue
Online——ZOOM
ZOOM INFO
ZOOM Link:
https://zoom.com.cn/j/68805004048 Conference ID: 68805004048
Password: 782463
Abstract
It was recognized soon after the pioneering works of Riemann and Stokes in the mid-nineteenth century that entropy increases as the gas flows across a shock wave for polyatomic gases. Around the 1940's Bethe and Weyl independently formulated the convexity condition for the equivalence of the compressibility of a shock and the entropy increase across it. This was subsequently generalized to the general system of hyperbolic conservation laws by Lax. The situation without convexity is interesting. The Russian school of Oleinik and Krushkov obtained complete results for scalar laws. It is understood now that the existence of entropy for a system is a constitutive hypothesis. Godunov established the relation between the existence of entropy and the symmetric structure of a system. There have been efforts to relate the admissibility conditions for shock waves to entropy production. For this, we offer a definitive result for shock waves in the Euler equations for compressible media. In this talk, we will survey the historical developments on general systems as well as some exact analysis for the Euler equations.
Bio
Professor Tai-Ping Liu is distinguished research fellow at Academia Sinica. He obtained his Ph.D. from the University of Michigan in 1973. He has held professorship positions at University of Maryland, New York University and Stanford University, where he is now an Emeritus Professor.
His research deals with nonlinear partial differential equations, hyperbolic conservation laws, shock waves, the Boltzmann equation, and equations of gas dynamics. Among his contributions in hyperbolic conservation laws are the introduction of the Liu entropy condition for the admissibility of weak solutions, the deterministic version of the Glimm scheme for the construction of solutions, and the Liu–Yang functional for the well-posedness theory. With Yu, he has initiated the quantitative analysis of the Boltzmann equation, and established the invariant manifold theory for the stationary Boltzmann equation. Liu also made pioneering contributions to conservation laws with sources, including relaxation phenomenon, vacuum in gas flows, stability and in stability of nozzle flows.
Liu is member of Academia Sinica, member of TWAS, fellow of American Mathematical Society, fellow of SIAM, recipient of Galileo Galilei Medal, and other honors. In 2002, he was an invited speaker at the International Congress of Mathematicians in Beijing.
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