## 諸分野のための数学研究会

開催情報 火曜日　10:30～11:30　数理科学研究科棟(駒場) 056号室 儀我美一、石村直之(一橋大学)、齊藤宣一、山本昌宏 http://coe.math.sci.hokudai.ac.jp/sympo/various/ 北海道大学のHPには、第1回(2005年6月22日)～第22回(2009年2月18日)の情報が掲載されております。

### 2017年10月24日(火)

10:30-11:30   数理科学研究科棟(駒場) 056号室
Christian Klingenberg 氏 (Würzburg University)
The initial value problem for the multidimensional system of gas dynamics may have infinitely many weak solutions (English)
[ 講演概要 ]
We consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states only, where one state lies on the lower and the other state on the upper half plane. The aim is to investigate if there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. In this lecture we will show that the solution of this Riemann problem for the 2-d isentropic Euler equations is non-unique (except if the solution is smooth). Next we are able to show that there exist Lipschitz data that may lead to infinitely many solutions even for the full system of Euler equations. This is joint work with Simon Markfelder.