The Cauchy problem for the periodic Kadomtsev--Petviashvili--II equation below $L^2$

Sebastian Herr, Robert Schippa, Nikolay Tzvetkov

We extend Bourgain's $L^2$-wellposedness result for the KP-II equation on ${\mathbb{T}}^2$ to initial data with negative Sobolev regularity. The key ingredient is a new linear $L^4$-…