Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation on cylindrical spaces

We prove that the Zakharov-Kuznetsov equation on cylindrical spaces is globally well-posed below the energy norm. As is known, local well-posedness below energy space was obtained by the first author. We adapt I-method to extend the solutions globally in time. Using modified energies, we obtain the polynomial bounds on the $H^s$ growth for the global solutions.