Mathematics colloquium under Action I.1.5 “Thematic Research Programmes”
28 05 2025
On 29 May 2025 (Thursday), the Faculty of Mathematics, Informatics and Mechanics will organise a colloquium with a lecture by eminent mathematician Alexis Vasseur (The University of Texas at Austin).
The lecture will be entitled “Stability of discontinuous flow for incompressible inviscid fluid”.
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.
This presentation will give 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.
The colloquium will be held on 29 May 2025 at 14:30 in room 2180 (room RW) of the Faculty of Mathematics, Informatics and Mechanics.