The Cauchy problem for the generalized Zakharov–Kuznetsov equation on modulation spaces

Abstract

We consider the Cauchy problem for the generalized Zakharov–Kuznetsov equation ∂tu+∂x1Δu=∂x1(um+1) on three and higher dimensions. We mainly study the local well-posedness and the small data global well-posedness in the modulation space M2,10(Rn) for m≥4 and n≥3. We also investigate the quartic case, i.e., m=3.