On the Cauchy problem for the Kadomtsev-Petviashvili equation
The author gives a global result for the Cauchy problem of the Kadomtsev- Petviashvili equation. The solution is globally well-posed for initial data in \(L^ 2(\mathbb{R}^ 2/\mathbb{Z}^ 2)\). The result is obtained on extending a local result (obtained by applying a Picard fixed point argument) to a global one with the help of the \(L^ 2\)-conservation law. The method is analogous to the one used for the Schrödinger and Korteweg-de Vries equations, and it is based on an analysis of multiple Fourier series.
scientific article; zbMATH DE number 464906