Academician Chen Shuxing Discusses the Two-Dimensional Riemann Problem

Chen Shuxing, an academician of the Chinese Academy of Sciences and professor at Fudan University was invited by the School of Mathematics and delivered a report about Two Dimensional Riemann Problems on the Peiyangyuan Campus of Tianjin University on June 6, 2019. Sun Xiaotao, Dean of the School of Mathematics, presided over the seminar.

Starting with the study of the Riemann problem of one dimensional nonlinear hyperbolic equation, Academician Chen Shuxing introduced the origin and significance of the Riemann problem, expounded the complete solution of one-dimensional Riemann problems with the Lax equivalence theorem, and summarized research methods, leading the audience to think about how to study two dimensional Riemann problems.

Because of the complexity of the zone and equation, the study of two-dimensional Riemann problems is far more difficult than the one-dimensional version. Chen Shuxing took the Riemann problem of the two-dimensional Euler equation system to explain current research methods and conclusions of two-dimensional Riemann problems in detail. While explaining mathematical equations, he emphasized the importance of physical background and numerical experiments in mathematical research. For this reason, Academician Chen summarized that the study of many practical problems in real life had application to the study of Riemann problems, such as dam collapse, shock reflection, back steps and so on.

Although Chen Shuxing enumerated some difficulties in the study of two-dimensional Riemann problems, he encouraged students to study hard and fear no obstacles in mathematics research.

By the School of Mathematics

Editors: Eva Yin & Doris Harrington& Zhang Saiya