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Stability of discontinuous flow for incompressible inviscid fluid
- Speaker(s)
- Alexis Vasseur
- Affiliation
- The University of Texas at Austin
- Language of the talk
- English
- Date
- May 29, 2025, 2:30 p.m.
- Room
- room 2180 (sala RW)
- Title in Polish
- Stability of discontinuous flow for incompressible inviscid fluid
- Seminar
- Colloquium Of MIM
The compressible Euler equation can lead to the emergence of shock discontinuities in finite time, notably observed behind supersonic planes. A very natural way to justify these singularities involves studying solutions as inviscid limits of Navier-Stokes solutions with evanescent viscosities. The mathematical study of this problem is however very difficult because of the destabilization effects of the viscosity.
Bianchini and Bressan proved the inviscid limit to small BV solutions using the so-called artificial viscosities (Annals of Math. 2005). However, achieving this limit with physical viscosities remained an open question up to our recent result together with Geng Chen and Moon-Jin Kang.
In this presentation, we will provide a basic overview of classical mathematical theories to compressible fluid mechanics and introduce the recent method of a-contraction with shifts. We will describe the basic ideas and difficulties involved in the study of physical inviscid limits in the context of the barotropic Euler.
