Well-posedness for the two dimensional generalized Zakharov–Kuznetsov equation in anisotropic weighted Sobolev spaces

We consider the well-posedness of the initial value problem associated to the k  -generalized Zakharov–Kuznetsov equation in fractional weighted Sobolev spaces Hs(R2)∩L2((|x|2r1+|y|2r2)dxdy), s,r1,r2∈Rs,r1,r2∈R. Our method of proof is based on the contraction mapping principle and it mainly relies on the well-posedness results recently obtained for this equation in the Sobolev spaces Hs(R2)Hs(R2) and a new pointwise commutator type formula involving the group induced by the linear part of the equation and the fractional anisotropic weights to be considered.