Workshop "Kinetic theory: Boltzmann, Fokker Planck - Balescu, Lenhard"

20 - 23 December
Wolfgang Pauli Institute (WPI) Vienna, University of Vienna, Vienna, Austria

• Francois Golse
  (Ecole Polytechnique)
  
  From N-Body Schrödinger to Euler-Poisson
  
  This talk presents a joint mean-field and classical limit by which the Euler-Poisson system is rigorously derived from the N-body 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.).
  
• Jakob Möller
  (University of Vienna)
  
  The Pauli-Poisson equation and its cassical limit
  
  The Pauli-Poisson equation is a semi-relativistic description of electrons under the influence of a given linear (strong) magnetic field and a self-consistent 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 Stern-Gerlach term of magnetic field and spin represented by the Pauli matrices. On the other hand the Pauli-Poiswell equation includes the self-consistent 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 Pauli-Poiswell equation offers a fully self-consistent description of spin-1/2-particles in the semi-relativistic regime. We introduce the equations and study the semiclassical limit of Pauli-Poisson towards a semi-relativistic Vlasov equation with Lorentz force coupled to the Poisson equation. We use Wigner transform methods and a mixed state formulation, extending the work of Lions-Paul and Markowich-Mauser on the semiclassical limit of the Schrödinger-Poisson equation. We also present a result on global weak solutions of the Pauli-Poiswell equation.
  
• Ivan Moyano
  (Université Côte-d'Azur)
  
  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
  (Observatoire de la Côte d'Azur)
  
  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 Vlasov-Poisson (VP) equation, by showing that in fact the Hamiltonian dynamics of VP can be approximated by a diffusion equation in velocity for the space-average distribution function.

For more information, please visit the webpage of the workshop.

This event is supported by the FWF Doctoral Program "Dissipation and Dispersion in Nonlinear PDEs".