Nonlinear Stability in <i>L<sup>p</sup></i> for a Confined System of Charged Particles
Nonlinear Stability in <i>L<sup>p</sup></i> for a Confined System of Charged Particles
We prove the nonlinear stability in Lp, with $1\le p\le 2$, of particular steady solutions of the Vlasov--Poisson system for charged particles in the whole space R6 . Our main tool is a functional associated to the relative entropy or Casimir-energy functional.