Hyperbolic system of conservation laws
|날짜Date||2019-03-22||시간Time||15:50 ~ 18:00|
|장소Place||Math. Bldg. 404||초청자Host||이동현|
|연사Speaker||Moon-Jin Kang||소속Affiliation||Sookmyung Women's Univ.|
|TOPIC||Hyperbolic system of conservation laws|
|소개 및 안내사항Content||제1부
Title: Hyperbolic system of conservation laws
Abstract: We will first study a core feature of Burgers equation, which is the simplest nonlinear transport equation. For this equation, the continuity of a smooth initial datum (most of cases) breaks down instantaneously as the time goes on. This can be a nice starting point to study the hyperbolic system of conservation laws. As the most important example of this system, we will briefly mentioned the compressible Euler system.
Title: Uniqueness of an entropy shock to the compressible Euler system in the class of vanishing physical viscosity limits.
Abstract: The most distinguished feature of the compressible Euler system is that an entropy shock, as a irreversible singularity, can be formed in finite time even for smooth initial data.
Due to the severe singularity of the shock, Chiodaroli, De Lellis and Kreml constructed infinitely many "spurious" solutions starting from the one shock.
Surprisingly, those spurious solutions are all entropic. Nonetheless, a long standing conjecture guarantees the uniqueness of the shock in the class of inviscid limits of solutions to the Navier- Stokes system.
In this talk. we will give an answer to the conjecture.
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