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Seminar on Mathematics for various disciplines
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
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2017/10/24
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Christian Klingenberg (Würzburg University)
The initial value problem for the multidimensional system of gas dynamics may have infinitely many weak solutions (English)
Christian Klingenberg (Würzburg University)
The initial value problem for the multidimensional system of gas dynamics may have infinitely many weak solutions (English)
[ Abstract ]
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.
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.
