Abstract: In this talk we will discuss recent results regarding local well-posedness for the generalized Zakharov–Kuznetsov equation. We prove a high-dimensional version of the Strichartz estimates for the unitary group associated with the free Zakharov-Kuznetsov equation. As a by-product, we deduce maximal estimates which allow us to prove local well-posedness for the generalized Zakharov-Kuznetsov equation in the whole subcritical case whenever d\ge 4, k\ge 4 complementing the recent results of Kinoshita and Herr-Kinoshita. Finally, we use some of those maximal estimates in order to prove pointwise convergence results for the flow of the generalized Zakharov–Kuznetsov equation in any dimension, in the same spirit of a recent manuscript by Compaan, Lucà and Staffilani.
Venue: Modalidad Vía Online.
Speaker: Felipe Linares
Affiliation: IMPA, Brasil
Coordinator: Gabrielle Nornberg