

Abstract for the talk at 18.07.2012 (16:30 h)
Colloquium of the Max Planck InstituteClaude Bardos (Laboratoire Jacques-Louis Lions, Paris VII)
About the Vlasov Dirac equation
This is a report on a ongoing work with Anne Nouri from Marseille and Thierry Paul from Polytechnique Palaiseau.
I dub the equation
<center class="math-display"> <img src="/fileadmin/lecture_img/tex_11743c0x.png" alt=" &#x222B; &#x2202; f + v &#x22C5;&#x2202; f - &#x2202; ( f(x,w,t)dw )&#x2202; f = 0 t x x v " class="math-display"></center> Vlasov Dirac because it is a Vlasov type equation where the standard potential has been replaced by the Dirac mass. This turns out to be an important problem for different reasons.1 It is genuine model for numerical simulation of plasmas.
2 It exhibit some singular stabilities \ unstabilities properties which can be more easily analyzed than the standard instabilities (Landau Damping and so on..) for the original Vlasov equation.
3 It is at the cross road between mean field derivations and WKB or Wigner asymptotics.