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Oberseminar AG Mathematische Modellierung
Montag, den 02.06.2025 um 17.00 Uhr in B7 - Raum 210
Vortrag von Anatole Gaudin (Clausthal) zum Thema „Well-posedness of the Magnetohydodynamical system in the critical setting“.
Abstract: In this talk, we are going to discuss the global-in-time well-posedness of the Magnetohydrodynamical (MHD) system for small initial datas in half-space and rough bouned domain. This is a natural extension of the Navier-Stokes system where the fluid is also subject to magnetic field (the particles constituing the fluid have a given charge.). Here we are particularly in a regime where neither the linear part (parabolic) or the non-linear part of system fully drive the system behavior. This ties up to the introduction of the appropriate functional setting of critical $L^1$-maximal regularity in Besov spaces. After, giving a descrippion of the system, as well as a motivation of functional framework, we provide a review of the linear Analysis, which is central to have a complete overview on the powerfulness of the $L^1$-maximal regularity-framework. The more likely standard $L^q(L^p)$ setting will also be investigated. If time permits, I will present higher-non-linear versions of the system incorporating the Hall-effect (H-MHD system) or even the Messner effect (London-H-MHD system) arising from quantum electrodynamics.