Lunedì 10 Febbraio 2025, alle ore 15:00 in Aula 3014 (3° Piano) - Edificio U5, il Prof. Pierangelo Marcati (GSSI) terrà il seguente seminario
Titolo: Finite energy weak solutions to the quantum Euler-Maxwell system, existence and stability
Abstract: We show the existence of global in time, finite energy weak solutions to the Quantum Euler-Maxwell system, also known as quantum magnetohydrodynamics (QMHD), for a large class of initial data that are slightly more regular than being of finite energy. Hydrodynamic models of this type have been used by Feynman and Ginzburg, Landau, Lifschits and Pitaevskii in the study of superconductivity. It is also a prototypical model for a quantum plasma, arising for instance in the description of dense astrophysical objects such as white dwarf stars. We first introduce some preliminary results we will need throughout the talk, as well as the precise notion of finite energy weak solutions, then we prove suitable dispersive estimates for weak solutions to the non-linear Maxwell-Schrödinger system. These estimates play a crucial role in order to rigorously derive the continuity and momentum equations via the Madelung type transformations. Hence as a byproduct, the Lorentz force is well defined. Therefore we show non trivial local-smoothing estimates for the Maxwell-Schrödinger syste and we use them to prove our main results concerning the QMHD system. Joint with Paolo Antonelli (GSSI) e Raffaele Scandone (Univ. Napoli Federico II).
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