Nonexistence of minimal mass blow-up solution for the 2D cubic Zakharov-Kuznetsov equation

For the 2D cubic (mass-critical) Zakharov-Kuznetsov equation, \begin{equation*} \partial_tφ+\partial_{x_1}(Δφ+φ^3)=0,\quad (t,x)\in [0,\infty)\times $\mathbb{R}$^{2}, \end{equation*} we prove that there exist no finite/infinite time blow-up solution with minimal mass in the energy space. This nonexistence result is in contrast to the one obtained by Martel-Merle-Raphaël [17] for the mass-critical generalized Korteweg-de Vries (gKdV) equation. The proof relies on a refined ODE argument related to the modulation theory and a modified energy-virial Lyapunov functional with a monotonicity property.