Derivation of Yudovich solutions of Incompressible Euler from the Vlasov-Poisson system

We derive the two dimensional incompressible Euler equation as a quasineutral limit of the Vlasov-Poisson equation using a modulated energy approach. We propose a strategy which enables to treat solutions where the gradient of the velocity is merely $\mathrm{B}\mathrm{M}\mathrm{O}$, in accordance to the celebrated Yudovich theorem.