Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation

We consider the modified Zakharov-Kuznetsov (mZK) equation in two space dimensions in both focusing and defocusing cases. Using the I-method, we prove the global well-posedness of the Hs solutions for s>34 for any data in the defocusing case and under the assumption that the mass of the initial data is less than the mass of the ground state solution of Δφ−φ+φ3=0 in the focusing case. This improves the global well-posedness result of Linares and Pastor [20].