On the regularity of solutions of the Cauchy problem for the Zakharov-Kuznetsov equation in Hölder norms

The problem of the interior regularity of generalized solutions of the Cauchy problem for the Zakharov-Kuznetsov equation is studied. The existence of Hölder-continuous derivatives of given solutions is established. The study is based on the properties of the fundamental solution of the corresponding linearized equation. © 2015, Pleiades Publishing, Ltd.