New Lower Bound for the Radius of Analyticity for the Modified 2D Zakharov–Kuznetsov Equation

ABSTRACT We consider the initial value problem associated to the 2D modified Zakharov‐Kuznetsov equation. For a class of initial data that is real analytic in a strip around the axis of the complex plane that have a fixed radius of spatial analyticity , we show that the uniform radius of spatial analyticity of solutions at time is bounded from below by as the time goes to infinity. This improves very recent works. Our strategy mainly relies on an almost conservation law in a modified Gevrey spaces, local smoothing estimates, maximal function estimates, Strichartz estimates, and Sobolev embedding.