Abstract for the talk at 18.07.2012 (16:30 h)

Colloquium of the Max Planck Institute
Claude 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=" &amp;#x222B; &amp;#x2202; f + v &amp;#x22C5;&amp;#x2202; f - &amp;#x2202; ( f(x,w,t)dw )&amp;#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 Vlasov Dirac because it is a Vlasov type equation where the standard potential has been replaced by the Dirac mass.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.