Well-Posedness for the Two-dimensional Zakharov-Kuznetsov Equation

Abstract

We show the global well-posedness for the two-dimensional Zakharov-Kuznetsov equation in $H^{s}({\mathbb{R}^2})$ when $\frac{11}{13}<s<1$ via the I-method. Additionally, local well-posedness for the symmetrized ZK equation in $ B^\frac{1}{2}_{2,1}(\mathbb{R}^2)$ is established by using atomic spaces.