Nonexistence of minimal mass blow-up solution for the 2D cubic
Zakharov-Kuznetsov equation
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_t\phi+\partial_{x_1}(\Delta \phi+\phi^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-Rapha\"el [17] for the mass-critical generalized Korteweg-de Vries …