Discontinuity of the Vlasov--Poisson Flow in $L_x^p{L}_v^{\infty }$

Ke Chen, In-Jee Jeong, Quoc-Hung Nguyen +1

We prove that solution maps of the Vlasov--Poisson equation are discontinuous at the zero initial datum in $X_p=L_x^p{L}_v^{\infty }$ for every $1\le p<\infty$, in $\mathbb{R}^{d} \tim…