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Francois Golse  Mon, 20. Dec 21, 12:00  
From NBody Schrödinger to EulerPoisson  
This talk presents a joint meanfield and classical limit by which the EulerPoisson system is rigorously derived from the Nbody Schrödinger equation with Coulomb interaction in space dimension 3. One of the key ingredients in this derivation is a remarkable inequality for the Coulomb potential which has been obtained by S. Serfaty in 2020 (Duke Math. J.). 2)  

Jakob Möller  Mon, 20. Dec 21, 12:30  
The PauliPoisson equation and its cassical limit  
The PauliPoisson equation is a semirelativistic description of electrons under the influence of a given linear (strong) magnetic field and a selfconsistent electric potential computed from the Poisson equation in 3 space dimensions. It is a system of two magnetic Schrödinger type equations for the two components of the spinor, coupled by the additional SternGerlach term of magnetic field and spin represented by the Pauli matrices. On the other hand the PauliPoiswell equation includes the selfconsistent description of the magnetic field by coupling it via a three Poisson equations with the Pauli current as source term to the Pauli equation. The PauliPoiswell equation offers a fully selfconsistent description of spin1/2particles in the semirelativistic regime. We introduce the equations and study the semiclassical limit of PauliPoisson towards a semirelativistic Vlasov equation with Lorentz force coupled to the Poisson equation. We use Wigner transform methods and a mixed state formulation, extending the work of LionsPaul and MarkowichMauser on the semiclassical limit of the SchrödingerPoisson equation. We also present a result on global weak solutions of the PauliPoiswell equation.  

Ivan Moyano  Mon, 20. Dec 21, 15:00  
Unique continuation, Carleman estimates and propagation of smallness with applications in observability  
Based on a series of works in collaboration with Gilles Lebeau and Nicolas Burq Propagation of smallness and control for heat equations (with Nicolas Burq, to appear in JEMS), Spectral Inequalities for the Schrödinger operator (with Gilles Lebeau). Propagation of smallness and spectral estimates (with Nicolas Burq) And the recent advances in propagation of smallness introduced by Logonuv and Malinnikova. A. Logunov and E. Malinnikova. Quantitative propagation of smallness for solutions of elliptic equations. Preprint, Arxiv, (arXiv:1711.10076), 2017 A. Logunov. Nodal sets of Laplace eigenfunctions : polynomial upper estimates of the Hausdorff measure. Ann. of Math. (2), 187(1):221–239, 2018.  

Nicolas Besse  Mon, 20. Dec 21, 15:30  
Trying to prove quasilinear theory in plasma physics  
The aim of quasilinear theory is to explain relaxation or saturation of kinetic instabilities governed by the VlasovPoisson (VP) equation, by showing that in fact the Hamiltonian dynamics of VP can be approximated by a diffusion equation in velocity for the spaceaverage distribution function.  

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