On Kato's smoothing effect for a fractional version of the Zakharov-Kuznetsov equation
On Kato's smoothing effect for a fractional version of the Zakharov-Kuznetsov equation
In this work, we study some regularity properties associated with the initial value problem (IVP)$\begin{align} \left\{ \begin{array}{ll} \partial_{t}u-\partial_{x_{1}}(-\Delta)^{\alpha/2} u+u\partial_{x_{1}}u = 0, \quad 0< \alpha\leq 2, & \\ u(x, 0) = u_{0}(x), \quad x = (x_{1}, x_{2}, \dots, x_{n})\in \mathbb{R}^{n}, \, n\geq 2, \quad t\in\mathbb{R}, & \ \end{array} \right. \end{align}\ \ …