| Abstract: |
| We investigate the blow-up dynamics for the $L^2$ critical two-dimensional Zakharov-Kuznetsov equation with initial data $u_0$ slightly exceeding the mass of the soliton solution $Q$, which satisfies $-\Delta Q + Q - Q^3 = 0$. Employing methodologies analogous to those used in the study of the gKdV equation of Martel, Merle and Raphael, we categorize the behavior of the solution into three outcomes: asymptotic stability, finite-time blow-up, or divergence from the soliton`s vicinity. The universal blow-up behavior that we find is slightly different from the conjecture of Klein, Roudenko and Stoilov, by deriving a non-trivial, computationally determinable constant for the blow-up rate, dependent on the two-dimensional soliton`s behavior. The construction of blow-up solution involves the bubbling of the solitary wave which ensures that it is stable. |
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