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 $B_{2,1}^{\frac{1}{2}}({\mathbb{R}}^2)$ is established by using atomic spaces.

27 pages

References in corpus (1)

• Well-posedness and scattering for the KP-II equation in a critical space