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math.AP2025
Global Well-Posedness and Blow-Up for the fifth order critical KP-I equation
Francisc Bozgan
In the current paper, we investigate the fifth order modified KP-I eqaution, namely \begin{equation*} \partial_t u-\partial_{x}^{5}u-\partial_{x}^{-1}\partial_{y}u+\partial_{x}(u^3…
math.AP2024
Blow-Up Dynamics for the critical case of the D Zakharov-Kuznetsov equation
Francisc Bozgan, Tej-Eddine Ghoul, Nader Masmoudi +1
We investigate the blow-up dynamics for the critical two-dimensional Zakharov-Kuznetsov equation \begin{equation*} \begin{cases} \partial_t u+\partial_{x_1} (Δu+u^3)=0, \mbox…
math.AP2019
Local wellposedness of the modified KP-I equations in periodic setting with small initial data
Francisc Bozgan
We prove local well-posedness of partially periodic and periodic modified KP-I equations, namely for $\partial_t u+(-1)^{\frac{l+1}{2}}\partial^l_x u-\partial_x^{-1}\partial_y^2 u+…