Oberseminar Numerische Mathematik / Scientific Computing
Bernd Einfeldt
On the Uniqueness and Existence of Discontinuities
Abstract:
Fluid flows are often modeled at the level of the Euler equations. The existence and uniqueness or multiplicity of solutions for the compressible Euler equations is however an open problem for over half a century. Von Karman made the assessment: "I donīt think that there is any reason, that if you put a problem in a form which has no physical meaning, there shall be not two solutions".
This talk looks at the existence and uniqueness of contact discontinuities (a surfaces across which the pressure and the normal velocity component are constant, but the density and/or the tangential velocity component are discontinuous) and shock discontinuities. The conjecture is that a real physical contact wave must be approximated, in contrast to a shock wave, as a finite width continuous transition layer. The existence, uniqueness and stability of finite width and discontinuous transition layer approximations for the Euler and Navier-Stokes equations are discussed.
| Datum: | 20.06.11 | Zeit: | 17:00 Uhr | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | Raum 031 im Erdgeschoss |