The Zakharov–Kuznetsov equation in weighted Sobolev spaces

In this work we consider the initial value problem (IVP) associated to the two dimensional Zakharov–Kuznetsov equationut+∂x3u+∂x∂y2u+u∂xu=0,(x,y)∈R2,t∈R,u(x,y,0)=u0(x,y).} We study the well-posedness of the IVP in the weighted Sobolev spacesHs(R2)∩L2((1+x2+y2)rdxdy),Hs(R2)∩L2((1+x2+y2)rdxdy), with s,r∈Rs,r∈R.